document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167587>Question 167587</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780078738302/algebrahomeworkh>Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve each system of equations:<BR>\n" );
document.write( "x+2y=12<BR>\n" );
document.write( "3y-4z=25<BR>\n" );
document.write( "x+6y+z=20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123509 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123509\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help<BR>\n" );
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document.write( "Solve each system of equations:<BR>\n" );
document.write( "x+2y=12<BR>\n" );
document.write( "3y-4z=25<BR>\n" );
document.write( "x+6y+z=20<BR>\n" );
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document.write( "There is no fast way to solving these problems, but I will show you, what I believe is the easiest way, how to solve these problems<BR>\n" );
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document.write( "First we have to solve for a variable, we will need to solve for \"y\" in each equation, since they all have a variable \"y\" ( It usually doesn't matter, but in this case it does.<BR>\n" );
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document.write( "First equation, x+2y=12. (solve for \"y\")<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B2y=12+ ALIGN=MIDDLE  ALT=\"+x%2B2y=12+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, We can solve for \"y\", first we will move the \"x\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B2y+=12+ ALIGN=MIDDLE  ALT=\"+x%2B2y+=12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x-x%2B2y+=12-x+ ALIGN=MIDDLE  ALT=\"+x-x%2B2y+=12-x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y++=12+-+x+ ALIGN=MIDDLE  ALT=\"+2y++=12+-+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can rearrange the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y++=12+-+x+ ALIGN=MIDDLE  ALT=\"+2y++=12+-+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y++=+-x%2B12+ ALIGN=MIDDLE  ALT=\"+2y++=+-x%2B12+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to solve for \"y\" we will divide each side by \"2\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y++=+-x%2B12+ ALIGN=MIDDLE  ALT=\"+2y++=+-x%2B12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y%2F2++=+%28-x%2B12%29%2F2+ ALIGN=MIDDLE  ALT=\"+2y%2F2++=+%28-x%2B12%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y++=+%28-x%2B12%29%2F2+ ALIGN=MIDDLE  ALT=\"+y++=+%28-x%2B12%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%2B12%29%2F2+ ALIGN=MIDDLE  ALT=\"+%28-x%2B12%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our first answer<BR>\n" );
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document.write( "Second equation solve for \"y\", 3y-4z=25<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y-4z=25+ ALIGN=MIDDLE  ALT=\"+3y-4z=25+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to move (-4z) to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y-4z=25+ ALIGN=MIDDLE  ALT=\"+3y-4z=25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y-4z+%2B+4z+=25+%2B+4z+ ALIGN=MIDDLE  ALT=\"+3y-4z+%2B+4z+=25+%2B+4z+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+25+%2B+4z+ ALIGN=MIDDLE  ALT=\"+3y+=+25+%2B+4z+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can rearrange the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+25+%2B+4z+ ALIGN=MIDDLE  ALT=\"+3y+=+25+%2B+4z+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+4z+%2B+25+ ALIGN=MIDDLE  ALT=\"+3y+=+4z+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to solve for \"y\" we will need to divide each side by \"3\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+4z+%2B+25+ ALIGN=MIDDLE  ALT=\"+3y+=+4z+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y%2F3+=+%284z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"+3y%2F3+=+%284z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%284z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"+y+=+%284z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"+%284z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is your second answer<BR>\n" );
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document.write( "Now let us solve the last equation for \"y\", x+6y+z=20<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B6y%2Bz=20+ ALIGN=MIDDLE  ALT=\"+x%2B6y%2Bz=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, first we will move the \"z\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B6y%2Bz=20+ ALIGN=MIDDLE  ALT=\"+x%2B6y%2Bz=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B6y%2Bz-z=20-z+ ALIGN=MIDDLE  ALT=\"+x%2B6y%2Bz-z=20-z+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B6y=20-z+ ALIGN=MIDDLE  ALT=\"+x%2B6y=20-z+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now let's move the \"x\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B6y=20-z+ ALIGN=MIDDLE  ALT=\"+x%2B6y=20-z+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x-x%2B6y=20-z-x+ ALIGN=MIDDLE  ALT=\"+x-x%2B6y=20-z-x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y=20-z-x+ ALIGN=MIDDLE  ALT=\"+6y=20-z-x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, let us rearrange the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y=20-z-x+ ALIGN=MIDDLE  ALT=\"+6y=20-z-x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y=+-x+-+z+%2B+20+ ALIGN=MIDDLE  ALT=\"+6y=+-x+-+z+%2B+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to solve for \"y\", we will divide both sides by \"6\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y=+-x+-+z+%2B+20+ ALIGN=MIDDLE  ALT=\"+6y=+-x+-+z+%2B+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y%2F6=+%28-x+-+z+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"+6y%2F6=+%28-x+-+z+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-x+-+z+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"+y+=+%28-x+-+z+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x+-+z+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"+%28-x+-+z+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our third answer<BR>\n" );
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document.write( "Now let us put all of our answers side by side<BR>\n" );
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document.write( "First, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%2B12%29%2F2+ ALIGN=MIDDLE  ALT=\"+%28-x%2B12%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Second, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"%284z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Third, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x+-+z+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"+%28-x+-+z+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since all three answers are equal to \"y\" all of them are equal to each other, first we have to have both \"x\" and \"z\" in all equations<BR>\n" );
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document.write( "First, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%2B12%29%2F2+ ALIGN=MIDDLE  ALT=\"+%28-x%2B12%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this has no \"z's\" so this equation would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%2B0z%2B12%29%2F2+ ALIGN=MIDDLE  ALT=\"+%28-x%2B0z%2B12%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Second, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"%284z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this has no \"x's\" so this equation would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%280x+%2B+4z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"+%280x+%2B+4z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Third, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x+-+z+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"+%28-x+-+z+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this already has both \"x\" and \"z\"<BR>\n" );
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document.write( "Here are the new equations<BR>\n" );
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document.write( "First, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%2B0z%2B12%29%2F2+ ALIGN=MIDDLE  ALT=\"+%28-x%2B0z%2B12%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Second, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280x+%2B+4z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"%280x+%2B+4z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Third, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x+-+z+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"+%28-x+-+z+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "All of them equal each other, first we will let the first two equations equal each other<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%2B0z%2B12%29%2F2+=+%280x+%2B+4z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"+%28-x%2B0z%2B12%29%2F2+=+%280x+%2B+4z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will use cross multiplication<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%2B0z%2B12%29%2F2+=+%280x+%2B+4z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"+%28-x%2B0z%2B12%29%2F2+=+%280x+%2B+4z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28-x%2B0z%2B12%29%2F2+=+%280x+%2B+4z+%2B+25%29%2Fhighlight%283%29+ ALIGN=MIDDLE  ALT=\"+highlight%28-x%2B0z%2B12%29%2F2+=+%280x+%2B+4z+%2B+25%29%2Fhighlight%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%2B0z%2B12%29%2Fhighlight%282%29+=+highlight%280x+%2B+4z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"+%28-x%2B0z%2B12%29%2Fhighlight%282%29+=+highlight%280x+%2B+4z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%2B0z%2B12%29%283%29+=+%282%29%280x+%2B+4z+%2B+25%29+ ALIGN=MIDDLE  ALT=\"+%28-x%2B0z%2B12%29%283%29+=+%282%29%280x+%2B+4z+%2B+25%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will rearrange the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%2B0z%2B12%29%283%29+=+%282%29%280x+%2B+4z+%2B+25%29+ ALIGN=MIDDLE  ALT=\"+%28-x%2B0z%2B12%29%283%29+=+%282%29%280x+%2B+4z+%2B+25%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283%29%28-x%2B0z%2B12%29+=+%282%29%280x+%2B+4z+%2B+25%29+ ALIGN=MIDDLE  ALT=\"+%283%29%28-x%2B0z%2B12%29+=+%282%29%280x+%2B+4z+%2B+25%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we can use the distribution method to solve even more,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283%29%28-x%2B0z%2B12%29+=+%282%29%280x+%2B+4z+%2B+25%29+ ALIGN=MIDDLE  ALT=\"+%283%29%28-x%2B0z%2B12%29+=+%282%29%280x+%2B+4z+%2B+25%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%283%29%28highlight%28-x%29%2B0z%2B12%29+=+highlight%282%29%28highlight%280x%29+%2B+4z+%2B+25%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%283%29%28-x%2Bhighlight%280z%29%2B12%29+=+highlight%282%29%280x+%2B+highlight%284z%29+%2B+25%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%283%29%28-x%2B0z%2Bhighlight%2812%29%29+=+highlight%282%29%280x+%2B+4z+%2B+highlight%2825%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Don't forget to use the positive, and negative signs<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3x+%2B+0z+%2B+36+=+0x+%2B+8z+%2B+50+ ALIGN=MIDDLE  ALT=\"+-3x+%2B+0z+%2B+36+=+0x+%2B+8z+%2B+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will move the (-3x) and \"0z\" to the right side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3x+%2B+0z+%2B+36+=+0x+%2B+8z+%2B+50+ ALIGN=MIDDLE  ALT=\"+-3x+%2B+0z+%2B+36+=+0x+%2B+8z+%2B+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3x+%2B+3x+%2B+0z+-0z+%2B+36+=+0x+%2B+3x+%2B+8z+-0z+%2B+50+ ALIGN=MIDDLE  ALT=\"+-3x+%2B+3x+%2B+0z+-0z+%2B+36+=+0x+%2B+3x+%2B+8z+-0z+%2B+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++36+=+3x+%2B+8z+%2B+50+ ALIGN=MIDDLE  ALT=\"++36+=+3x+%2B+8z+%2B+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we will move the \"50\" to the left side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++36+=+3x+%2B+8z+%2B+50+ ALIGN=MIDDLE  ALT=\"++36+=+3x+%2B+8z+%2B+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++36+-+50+=+3x+%2B+8z+%2B+50+-+50+ ALIGN=MIDDLE  ALT=\"++36+-+50+=+3x+%2B+8z+%2B+50+-+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-14+=+3x+%2B+8z+ ALIGN=MIDDLE  ALT=\"++-14+=+3x+%2B+8z+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, rearranging we get<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-14+=+3x+%2B+8z+ ALIGN=MIDDLE  ALT=\"++-14+=+3x+%2B+8z+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+%2B+8z+=+-14+ ALIGN=MIDDLE  ALT=\"++3x+%2B+8z+=+-14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+%2B+8z+=+-14+ ALIGN=MIDDLE  ALT=\"++3x+%2B+8z+=+-14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our first answer<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now we can use the last two equations ( we can use the middle equation twice<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Second, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280x+%2B+4z+%2B+25%29%2F3+ ALIGN=MIDDLE  ALT=\"%280x+%2B+4z+%2B+25%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Third, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x+-+z+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"+%28-x+-+z+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%280x+%2B+4z+%2B+25%29%2F3+=+%28-x+-+z+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"+%280x+%2B+4z+%2B+25%29%2F3+=+%28-x+-+z+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can use cross multiplication<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%280x+%2B+4z+%2B+25%29%2F3+=+%28-x+-+z+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"+%280x+%2B+4z+%2B+25%29%2F3+=+%28-x+-+z+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%280x+%2B+4z+%2B+25%29%2F3+=+%28-x+-+z+%2B+20%29%2Fhighlight%286%29+ ALIGN=MIDDLE  ALT=\"+highlight%280x+%2B+4z+%2B+25%29%2F3+=+%28-x+-+z+%2B+20%29%2Fhighlight%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%280x+%2B+4z+%2B+25%29%2Fhighlight%283%29+=+highlight%28-x+-+z+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"+%280x+%2B+4z+%2B+25%29%2Fhighlight%283%29+=+highlight%28-x+-+z+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%280x+%2B+4z+%2B+25%29%286%29+=+%283%29%28-x-z%2B20%29+ ALIGN=MIDDLE  ALT=\"+%280x+%2B+4z+%2B+25%29%286%29+=+%283%29%28-x-z%2B20%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, rearranging the left side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%280x+%2B+4z+%2B+25%29%286%29+=+%283%29%28-x-z%2B20%29+ ALIGN=MIDDLE  ALT=\"+%280x+%2B+4z+%2B+25%29%286%29+=+%283%29%28-x-z%2B20%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%29%280x+%2B+4z+%2B+25%29+=+%283%29%28-x-z%2B20%29+ ALIGN=MIDDLE  ALT=\"+%286%29%280x+%2B+4z+%2B+25%29+=+%283%29%28-x-z%2B20%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will use the distrubution method,<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%286%29%28highlight%280x%29+%2B+4z+%2B+25%29+=+highlight%283%29%28highlight%28-x%29-z%2B20%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%286%29%280x+%2B+highlight%284z%29+%2B+25%29+=+highlight%283%29%28-x-highlight%28z%29%2B20%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%286%29%280x+%2B+4z+%2B+highlight%2825%29%29+=+highlight%283%29%28-x-z%2Bhighlight%2820%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Remember the signs, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0x+%2B+24z+%2B+150+=+-3x-3z%2B60+ ALIGN=MIDDLE  ALT=\"+0x+%2B+24z+%2B+150+=+-3x-3z%2B60+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will move \"-3x\" to the left side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0x+%2B+24z+%2B+150+=+-3x-3z%2B60+ ALIGN=MIDDLE  ALT=\"+0x+%2B+24z+%2B+150+=+-3x-3z%2B60+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0x%2B3x+%2B+24z+%2B+150+=+-3x%2B3x-3z%2B60+ ALIGN=MIDDLE  ALT=\"+0x%2B3x+%2B+24z+%2B+150+=+-3x%2B3x-3z%2B60+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+24z+%2B+150+=+-3z%2B60+ ALIGN=MIDDLE  ALT=\"+3x+%2B+24z+%2B+150+=+-3z%2B60+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will now move \"-3z to the left side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+24z+%2B+150+=+-3z%2B60+ ALIGN=MIDDLE  ALT=\"+3x+%2B+24z+%2B+150+=+-3z%2B60+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+24z%2B3z+%2B+150+=+-3z%2B3z%2B60+ ALIGN=MIDDLE  ALT=\"+3x+%2B+24z%2B3z+%2B+150+=+-3z%2B3z%2B60+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+27z+%2B+150+=+60+ ALIGN=MIDDLE  ALT=\"+3x+%2B+27z+%2B+150+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will lastly move \"150\" to the right side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+27z+%2B+150+=+60+ ALIGN=MIDDLE  ALT=\"+3x+%2B+27z+%2B+150+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+27z+%2B+150+-+150++=+60+-+150+ ALIGN=MIDDLE  ALT=\"+3x+%2B+27z+%2B+150+-+150++=+60+-+150+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+27z+=+-90+ ALIGN=MIDDLE  ALT=\"+3x+%2B+27z+=+-90+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+27z+=+-90+ ALIGN=MIDDLE  ALT=\"+3x+%2B+27z+=+-90+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the second answer, once again let us put our two answers side by side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "First, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+%2B+8z+=+-14+ ALIGN=MIDDLE  ALT=\"++3x+%2B+8z+=+-14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Second, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+27z+=+-90+ ALIGN=MIDDLE  ALT=\"+3x+%2B+27z+=+-90+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can reduce this equation by dividing each side by \"3\", <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+27z+=+-90+ ALIGN=MIDDLE  ALT=\"+3x+%2B+27z+=+-90+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283x+%2B+27z%29%2F3+=+-90%2F3+ ALIGN=MIDDLE  ALT=\"+%283x+%2B+27z%29%2F3+=+-90%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283x%2F3%29+%2B+%2827z%2F3%29+=+-30+ ALIGN=MIDDLE  ALT=\"+%283x%2F3%29+%2B+%2827z%2F3%29+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+9z+=+-30+ ALIGN=MIDDLE  ALT=\"+x+%2B+9z+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Our new equations are<BR>\n" );
document.write( ".<BR>\n" );
document.write( "First, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+%2B+8z+=+-14+ ALIGN=MIDDLE  ALT=\"++3x+%2B+8z+=+-14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Second, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+9z+=+-30+ ALIGN=MIDDLE  ALT=\"+x+%2B+9z+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now we need to solve for a variable again, doesn't matter which one, we will solve for \"x\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "First, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+%2B+8z+=+-14+ ALIGN=MIDDLE  ALT=\"++3x+%2B+8z+=+-14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to move \"8z\" to the right side,<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+%2B+8z+=+-14+ ALIGN=MIDDLE  ALT=\"++3x+%2B+8z+=+-14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+%2B+8z+-+8z+=++-14-8z+ ALIGN=MIDDLE  ALT=\"++3x+%2B+8z+-+8z+=++-14-8z+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+=++-14-8z+ ALIGN=MIDDLE  ALT=\"++3x+=++-14-8z+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Rearranging the right side, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+=++-14-8z+ ALIGN=MIDDLE  ALT=\"++3x+=++-14-8z+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+=++-8z-14+ ALIGN=MIDDLE  ALT=\"++3x+=++-8z-14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can solve for \"x\" by dividing each side by \"3\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+=++-8z-14+ ALIGN=MIDDLE  ALT=\"++3x+=++-8z-14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x%2F3+=++%28-8z-14%29%2F3+ ALIGN=MIDDLE  ALT=\"++3x%2F3+=++%28-8z-14%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++x+=++%28-8z-14%29%2F3+ ALIGN=MIDDLE  ALT=\"++x+=++%28-8z-14%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-8z-14%29%2F3+ ALIGN=MIDDLE  ALT=\"++%28-8z-14%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our first answer<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We can now solve for \"x\" in the second equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+9z+=+-30+ ALIGN=MIDDLE  ALT=\"+x+%2B+9z+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+9z+=+-30+ ALIGN=MIDDLE  ALT=\"+x+%2B+9z+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will move \"9z\" to the right side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+9z+=+-30+ ALIGN=MIDDLE  ALT=\"+x+%2B+9z+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+9z-9z+=+-30-9z+ ALIGN=MIDDLE  ALT=\"+x+%2B+9z-9z+=+-30-9z+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-30-9z+ ALIGN=MIDDLE  ALT=\"+x+=+-30-9z+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, rearranging the right side, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-30-9z+ ALIGN=MIDDLE  ALT=\"+x+=+-30-9z+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-9z-30 ALIGN=MIDDLE  ALT=\"+x+=+-9z-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9z-30 ALIGN=MIDDLE  ALT=\"+-9z-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our second answer, let us put our two answers together<BR>\n" );
document.write( ".<BR>\n" );
document.write( "First, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-8z-14%29%2F3+ ALIGN=MIDDLE  ALT=\"++%28-8z-14%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Second, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9z-30 ALIGN=MIDDLE  ALT=\"+-9z-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since our two answers equal \"x\" they will equal each other<BR>\n" );
document.write( ".<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-8z-14%29%2F3+=+-9z-30+ ALIGN=MIDDLE  ALT=\"++%28-8z-14%29%2F3+=+-9z-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-8z-14%29%2F3+=+%28-9z-30%29%2F1+ ALIGN=MIDDLE  ALT=\"++%28-8z-14%29%2F3+=+%28-9z-30%29%2F1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using cross-multiplication<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++highlight%28-8z-14%29%2F3+=+%28-9z-30%29%2Fhighlight%281%29+ ALIGN=MIDDLE  ALT=\"++highlight%28-8z-14%29%2F3+=+%28-9z-30%29%2Fhighlight%281%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-8z-14%29%2Fhighlight%283%29+=+highlight%28-9z-30%29%2F1+ ALIGN=MIDDLE  ALT=\"++%28-8z-14%29%2Fhighlight%283%29+=+highlight%28-9z-30%29%2F1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-8z-14%29%281%29+=+%283%29%28-9z-30%29+ ALIGN=MIDDLE  ALT=\"+%28-8z-14%29%281%29+=+%283%29%28-9z-30%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, rearranging the left side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-8z-14%29%281%29+=+%283%29%28-9z-30%29+ ALIGN=MIDDLE  ALT=\"+%28-8z-14%29%281%29+=+%283%29%28-9z-30%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%29%28-8z-14%29+=+%283%29%28-9z-30%29+ ALIGN=MIDDLE  ALT=\"+%281%29%28-8z-14%29+=+%283%29%28-9z-30%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using distribution<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%281%29%28highlight%28-8z%29-14%29+=+highlight%283%29%28highlight%28-9z%29-30%29+ ALIGN=MIDDLE  ALT=\"+highlight%281%29%28highlight%28-8z%29-14%29+=+highlight%283%29%28highlight%28-9z%29-30%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%281%29%28-8z-highlight%2814%29%29+=+highlight%283%29%28-9z-highlight%2830%29%29+ ALIGN=MIDDLE  ALT=\"+highlight%281%29%28-8z-highlight%2814%29%29+=+highlight%283%29%28-9z-highlight%2830%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Remember the signs, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8z+-+14+=+-27z+-+90+ ALIGN=MIDDLE  ALT=\"+-8z+-+14+=+-27z+-+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will now solve for \"z\", we will move (-27z) to the left side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8z+-+14+=+-27z+-+90+ ALIGN=MIDDLE  ALT=\"+-8z+-+14+=+-27z+-+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8z%2B27z+-+14+=+-27z%2B+27z+-+90+ ALIGN=MIDDLE  ALT=\"+-8z%2B27z+-+14+=+-27z%2B+27z+-+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+19z+-+14+=++-+90+ ALIGN=MIDDLE  ALT=\"+19z+-+14+=++-+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we will move (-14) to the right side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+19z+-+14+=++-+90+ ALIGN=MIDDLE  ALT=\"+19z+-+14+=++-+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+19z+-+14%2B14+=++-+90%2B14+ ALIGN=MIDDLE  ALT=\"+19z+-+14%2B14+=++-+90%2B14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+19z+=++-+76+ ALIGN=MIDDLE  ALT=\"+19z+=++-+76+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to solve \"z\" we will divide each side by \"19\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+19z+=++-+76+ ALIGN=MIDDLE  ALT=\"+19z+=++-+76+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+19z%2F19+=++-+76%2F19+ ALIGN=MIDDLE  ALT=\"+19z%2F19+=++-+76%2F19+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=++-+4+ ALIGN=MIDDLE  ALT=\"+z+=++-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to check our answer we will replace \"z\" with (-4) in our equation<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-8z-14%29%2F3+=+-9z-30+ ALIGN=MIDDLE  ALT=\"++%28-8z-14%29%2F3+=+-9z-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-8%28-4%29-14%29%2F3+=+-9%28-4%29-30+ ALIGN=MIDDLE  ALT=\"++%28-8%28-4%29-14%29%2F3+=+-9%28-4%29-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28%2832%29-14%29%2F3+=+%2836%29-30+ ALIGN=MIDDLE  ALT=\"++%28%2832%29-14%29%2F3+=+%2836%29-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%2818%29%2F3+=+%286%29+ ALIGN=MIDDLE  ALT=\"++%2818%29%2F3+=+%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%286%29+=+%286%29+ ALIGN=MIDDLE  ALT=\"++%286%29+=+%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now that we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=+-4+ ALIGN=MIDDLE  ALT=\"+z+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can replace it in one of the equations with two variables<BR>\n" );
document.write( ".<BR>\n" );
document.write( "First, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++3x+%2B+8z+=+-14+ ALIGN=MIDDLE  ALT=\"++3x+%2B+8z+=+-14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Second, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+9z+=+-30+ ALIGN=MIDDLE  ALT=\"+x+%2B+9z+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "We will use the second equation, replace \"z\" with (-4)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+9z+=+-30+ ALIGN=MIDDLE  ALT=\"+x+%2B+9z+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+9%28-4%29+=+-30+ ALIGN=MIDDLE  ALT=\"+x+%2B+9%28-4%29+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+%28-36%29+=+-30+ ALIGN=MIDDLE  ALT=\"+x+%2B+%28-36%29+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x++-36++=+-30+ ALIGN=MIDDLE  ALT=\"+x++-36++=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, lets move (-36) to the right side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x++-36++=+-30+ ALIGN=MIDDLE  ALT=\"+x++-36++=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x++-36%2B36++=+-30%2B36+ ALIGN=MIDDLE  ALT=\"+x++-36%2B36++=+-30%2B36+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x++=+6+ ALIGN=MIDDLE  ALT=\"+x++=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's check our answer by replacing \"x\" with \"6\", and \"z\" with (-4) in the equation,<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+9z+=+-30+ ALIGN=MIDDLE  ALT=\"+x+%2B+9z+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%29+%2B+9%28-4%29+=+-30+ ALIGN=MIDDLE  ALT=\"+%286%29+%2B+9%28-4%29+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+%2B+%28-36%29+=+-30+ ALIGN=MIDDLE  ALT=\"+6+%2B+%28-36%29+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+-+36+=+-30+ ALIGN=MIDDLE  ALT=\"+6+-+36+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-30+=+-30+ ALIGN=MIDDLE  ALT=\"+-30+=+-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "\"x\" = \"6\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "\"z\" = (-4),<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now we can find \"y\" by replacing \"x\" and \"y\" in one of the three original equations<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x+2y=12<BR>\n" );
document.write( "3y-4z=25<BR>\n" );
document.write( "x+6y+z=20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We will need to use the third equation, replace \"x\" with \"6\", \"z\" with (-4)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B6y%2Bz=20+ ALIGN=MIDDLE  ALT=\"+x%2B6y%2Bz=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%29%2B6y%2B%28-4%29=20+ ALIGN=MIDDLE  ALT=\"+%286%29%2B6y%2B%28-4%29=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%29%2B6y-+4=20+ ALIGN=MIDDLE  ALT=\"+%286%29%2B6y-+4=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6-4%2B6y=20+ ALIGN=MIDDLE  ALT=\"+6-4%2B6y=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2B6y=20+ ALIGN=MIDDLE  ALT=\"+2%2B6y=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will move \"2\" to the right side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2B6y=20+ ALIGN=MIDDLE  ALT=\"+2%2B6y=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2-2%2B6y=20-2+ ALIGN=MIDDLE  ALT=\"+2-2%2B6y=20-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y=+18+ ALIGN=MIDDLE  ALT=\"+6y=+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to find \"y\", divide each side by \"6\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y=+18+ ALIGN=MIDDLE  ALT=\"+6y=+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y%2F6=+18%2F6+ ALIGN=MIDDLE  ALT=\"+6y%2F6=+18%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3+ ALIGN=MIDDLE  ALT=\"+y+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can check by replacing \"x\" with \"6\", \"y\" with \"3\", \"z\" with (-4) in the equation<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B6y%2Bz=20+ ALIGN=MIDDLE  ALT=\"+x%2B6y%2Bz=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%29%2B6%283%29%2B%28-4%29=20+ ALIGN=MIDDLE  ALT=\"+%286%29%2B6%283%29%2B%28-4%29=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2B18-4=20+ ALIGN=MIDDLE  ALT=\"+6%2B18-4=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+24-4=20+ ALIGN=MIDDLE  ALT=\"+24-4=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20=20+ ALIGN=MIDDLE  ALT=\"+20=20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( True )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( ".<BR>\n" );
document.write( "z = (-4)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We can check by replacing the other two original equations<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B2y=12+ ALIGN=MIDDLE  ALT=\"+x%2B2y=12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%29%2B2%283%29=12+ ALIGN=MIDDLE  ALT=\"+%286%29%2B2%283%29=12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2B6=12+ ALIGN=MIDDLE  ALT=\"+6%2B6=12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12+=+12+ ALIGN=MIDDLE  ALT=\"+12+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y-4z=25+ ALIGN=MIDDLE  ALT=\"+3y-4z=25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%283%29-4%28-4%29=25+ ALIGN=MIDDLE  ALT=\"+3%283%29-4%28-4%29=25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9%2B+16=25+ ALIGN=MIDDLE  ALT=\"+9%2B+16=25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25+=+25+ ALIGN=MIDDLE  ALT=\"+25+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( ".<BR>\n" );
document.write( "z = (-4)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "ordered pairs are given as (x,y,z), our ordered pair = ( 6,3,-4)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope I helped, Levi </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );