document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177344>Question 177344</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve this system of equations\r<BR>\n" );
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document.write( " 3x+4y+z=7<BR>\n" );
document.write( "    2y+z=3<BR>\n" );
document.write( "-5x+3y+8z=-31 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132432 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=132432\">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 this system of equations<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%283x%2B4y%2Bz=7%2C+2y%2Bz=3%2C+-5x%2B3y%2B8z=-31+%29+ ALIGN=MIDDLE  ALT=\"+system+%283x%2B4y%2Bz=7%2C+2y%2Bz=3%2C+-5x%2B3y%2B8z=-31+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This system is a little easier than what we would have to do, but is the same concept<BR>\n" );
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document.write( "We need to solve for one letter in one of the equations, doesn't matter which one, or which equation, we will solve for \"z\" in the second equation, since it will be the easiest<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+%2B+z+=+3+ ALIGN=MIDDLE  ALT=\"+2y+%2B+z+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to solve \"z\", we will move \"2y\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+%2B+z+=+3+ ALIGN=MIDDLE  ALT=\"+2y+%2B+z+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+-+2y+%2B+z+=+3+-+2y+ ALIGN=MIDDLE  ALT=\"+2y+-+2y+%2B+z+=+3+-+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=+3+-+2y+ ALIGN=MIDDLE  ALT=\"+z+=+3+-+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=++%28-2y%29+%2B+3+ ALIGN=MIDDLE  ALT=\"+z+=++%28-2y%29+%2B+3+\"   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=+z+=++%28-2y%29+%2B+3+ ALIGN=MIDDLE  ALT=\"+z+=++%28-2y%29+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now that we found \"z\", we can replace \"z\" with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2y%29+%2B+3+ ALIGN=MIDDLE  ALT=\"+%28-2y%29+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the other two equations<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%283x%2B4y%2Bz=7%2C+-5x%2B3y%2B8z=-31+%29+ ALIGN=MIDDLE  ALT=\"+system+%283x%2B4y%2Bz=7%2C+-5x%2B3y%2B8z=-31+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "replace \"z\" with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2y%29+%2B+3+ ALIGN=MIDDLE  ALT=\"+%28-2y%29+%2B+3+\"   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=+3x%2B4y%2Bz=7+ ALIGN=MIDDLE  ALT=\"+3x%2B4y%2Bz=7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B4y%2B%28%28-2y%29+%2B+3+%29=7+ ALIGN=MIDDLE  ALT=\"+3x%2B4y%2B%28%28-2y%29+%2B+3+%29=7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now just combine like terms<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B4y%2B%28%28-2y%29+%2B+3+%29=7+ ALIGN=MIDDLE  ALT=\"+3x%2B4y%2B%28%28-2y%29+%2B+3+%29=7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B4y%2B%28-2y%29+%2B+3+=7+ ALIGN=MIDDLE  ALT=\"+3x%2B4y%2B%28-2y%29+%2B+3+=7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B4y+-2y+%2B+3+=7+ ALIGN=MIDDLE  ALT=\"+3x%2B4y+-2y+%2B+3+=7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B+2y+%2B+3+=7+ ALIGN=MIDDLE  ALT=\"+3x%2B+2y+%2B+3+=7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we will move \"3\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B+2y+%2B+3+=7+ ALIGN=MIDDLE  ALT=\"+3x%2B+2y+%2B+3+=7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B+2y+%2B+3+-+3+=7+-+3+ ALIGN=MIDDLE  ALT=\"+3x%2B+2y+%2B+3+-+3+=7+-+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B+2y+=4+ ALIGN=MIDDLE  ALT=\"+3x%2B+2y+=4+\"   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=+3x%2B+2y+=4+ ALIGN=MIDDLE  ALT=\"+3x%2B+2y+=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our first answer<BR>\n" );
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document.write( "Now lets replace \"z\" in the other equation<BR>\n" );
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document.write( "replace \"z\" with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2y%29+%2B+3+ ALIGN=MIDDLE  ALT=\"+%28-2y%29+%2B+3+\"   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=++-5x%2B3y%2B8z=-31++ ALIGN=MIDDLE  ALT=\"++-5x%2B3y%2B8z=-31++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x%2B3y%2B8%28%28-2y%29+%2B+3%29=-31++ ALIGN=MIDDLE  ALT=\"++-5x%2B3y%2B8%28%28-2y%29+%2B+3%29=-31++\"   DISABLED_style= \"max-width:90%; height:auto;\" >, once again just combine like terms, we will use the distributive property to solve even more<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x%2B3y%2B8%28%28-2y%29+%2B+3%29=-31++ ALIGN=MIDDLE  ALT=\"++-5x%2B3y%2B8%28%28-2y%29+%2B+3%29=-31++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x%2B3y%2Bhighlight%288%29%28highlight%28-2y%29+%2B+3%29=-31++ ALIGN=MIDDLE  ALT=\"++-5x%2B3y%2Bhighlight%288%29%28highlight%28-2y%29+%2B+3%29=-31++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x%2B3y%2Bhighlight%288%29%28-2y+%2B+highlight%283%29%29=-31++ ALIGN=MIDDLE  ALT=\"++-5x%2B3y%2Bhighlight%288%29%28-2y+%2B+highlight%283%29%29=-31++\"   DISABLED_style= \"max-width:90%; height:auto;\" >, remember the negative/positive signs<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x%2B3y%2B%28-16y%29+%2B+24+=-31++ ALIGN=MIDDLE  ALT=\"++-5x%2B3y%2B%28-16y%29+%2B+24+=-31++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x%2B3y+-+16y+%2B+24+=-31++ ALIGN=MIDDLE  ALT=\"++-5x%2B3y+-+16y+%2B+24+=-31++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x+-+13y+%2B+24+=-31++ ALIGN=MIDDLE  ALT=\"++-5x+-+13y+%2B+24+=-31++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "now we will move \"24\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x+-+13y+%2B+24+=-31++ ALIGN=MIDDLE  ALT=\"++-5x+-+13y+%2B+24+=-31++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x+-+13y+%2B+24+-+24+=-31+-+24++ ALIGN=MIDDLE  ALT=\"++-5x+-+13y+%2B+24+-+24+=-31+-+24++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x+-+13y++=-+55++ ALIGN=MIDDLE  ALT=\"++-5x+-+13y++=-+55++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will make everything positive by multiplying each side by (-1)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-5x+-+13y++=-+55++ ALIGN=MIDDLE  ALT=\"++-5x+-+13y++=-+55++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-1%29%28-5x+-+13y%29++=%28-1%29%28-+55%29++ ALIGN=MIDDLE  ALT=\"++%28-1%29%28-5x+-+13y%29++=%28-1%29%28-+55%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will use the distribution method<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28-1%29%28-5x+-+13y%29++=%28-1%29%28-+55%29++ ALIGN=MIDDLE  ALT=\"++%28-1%29%28-5x+-+13y%29++=%28-1%29%28-+55%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++highlight%28-1%29%28highlight%28-5x%29+-+13y%29++=%28-1%29%28-+55%29++ ALIGN=MIDDLE  ALT=\"++highlight%28-1%29%28highlight%28-5x%29+-+13y%29++=%28-1%29%28-+55%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++highlight%28-1%29%28-5x+-+highlight%2813y%29%29++=%28-1%29%28-+55%29++ ALIGN=MIDDLE  ALT=\"++highlight%28-1%29%28-5x+-+highlight%2813y%29%29++=%28-1%29%28-+55%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" >, remember the signs<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++5x+%2B+13y++=%28-1%29%28-+55%29++ ALIGN=MIDDLE  ALT=\"++5x+%2B+13y++=%28-1%29%28-+55%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++5x+%2B+13y++=+55++ ALIGN=MIDDLE  ALT=\"++5x+%2B+13y++=+55++\"   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=++5x+%2B+13y++=+55++ ALIGN=MIDDLE  ALT=\"++5x+%2B+13y++=+55++\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our second answer<BR>\n" );
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document.write( "We will now put these two answers into a system<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%283x%2B+2y+=4%2C+5x+%2B+13y++=+55%29+ ALIGN=MIDDLE  ALT=\"+system+%283x%2B+2y+=4%2C+5x+%2B+13y++=+55%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To make it easier, we will avoid fractions as much as possible<BR>\n" );
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document.write( "We will multiply the first equation by \"5\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2B+2y+=4+ ALIGN=MIDDLE  ALT=\"+3x%2B+2y+=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%283x%2B+2y%29+=5%284%29+ ALIGN=MIDDLE  ALT=\"+5%283x%2B+2y%29+=5%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%283x%2B+2y%29+=+20+ ALIGN=MIDDLE  ALT=\"+5%283x%2B+2y%29+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using distribution<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%283x%2B+2y%29+=+20+ ALIGN=MIDDLE  ALT=\"+5%283x%2B+2y%29+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%285%29%28highlight%283x%29%2B+2y%29+=+20+ ALIGN=MIDDLE  ALT=\"+highlight%285%29%28highlight%283x%29%2B+2y%29+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%285%29%283x%2B+highlight%282y%29%29+=+20+ ALIGN=MIDDLE  ALT=\"+highlight%285%29%283x%2B+highlight%282y%29%29+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,remember signs, = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15x%2B+10y+=+20+ ALIGN=MIDDLE  ALT=\"+15x%2B+10y+=+20+\"   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=+15x%2B+10y+=+20+ ALIGN=MIDDLE  ALT=\"+15x%2B+10y+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the new equation<BR>\n" );
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document.write( "Now we will multiply the second equation by \"3\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x+%2B+13y++=+55+ ALIGN=MIDDLE  ALT=\"+5x+%2B+13y++=+55+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%285x+%2B+13y%29++=+3%2855%29+ ALIGN=MIDDLE  ALT=\"+3%285x+%2B+13y%29++=+3%2855%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%285x+%2B+13y%29++=+165+ ALIGN=MIDDLE  ALT=\"+3%285x+%2B+13y%29++=+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using distribution<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%285x+%2B+13y%29++=+165+ ALIGN=MIDDLE  ALT=\"+3%285x+%2B+13y%29++=+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%283%29%28highlight%285x%29+%2B+13y%29++=+165+ ALIGN=MIDDLE  ALT=\"+highlight%283%29%28highlight%285x%29+%2B+13y%29++=+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%283%29%285x+%2B+highlight%2813y%29%29++=+165+ ALIGN=MIDDLE  ALT=\"+highlight%283%29%285x+%2B+highlight%2813y%29%29++=+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, remembering signs, = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15x+%2B+39y++=+165+ ALIGN=MIDDLE  ALT=\"+15x+%2B+39y++=+165+\"   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=+15x+%2B+39y++=+165+ ALIGN=MIDDLE  ALT=\"+15x+%2B+39y++=+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the new equation<BR>\n" );
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document.write( "We will put the two new equations in the system<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%28+15x+%2B+39y++=+165%2C+15x%2B+10y+=+20+%29+ ALIGN=MIDDLE  ALT=\"+system+%28+15x+%2B+39y++=+165%2C+15x%2B+10y+=+20+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will now use elimination to find \"y\", we will subtract the bottom equation from the top equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++15x+%2B+39y++=+165+ ALIGN=MIDDLE  ALT=\"++15x+%2B+39y++=+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15x%2B+10y+=+20++ ALIGN=MIDDLE  ALT=\"+15x%2B+10y+=+20++\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the negative sign makes all the numbers negative<BR>\n" );
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document.write( "Now we need to add the equations<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%28+15x+%2B+39y++=+165%2C+-15x+-+10y+=+-+20%29+%29+ ALIGN=MIDDLE  ALT=\"+system+%28+15x+%2B+39y++=+165%2C+-15x+-+10y+=+-+20%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "________________\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0x+%2B+29y+=+145+ ALIGN=MIDDLE  ALT=\"+0x+%2B+29y+=+145+\"   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=+0x+%2B+29y+=+145+ ALIGN=MIDDLE  ALT=\"+0x+%2B+29y+=+145+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+29y+=+145+ ALIGN=MIDDLE  ALT=\"+29y+=+145+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to find \"y\" we will divide each side by \"29\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+29y+=+145+ ALIGN=MIDDLE  ALT=\"+29y+=+145+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+29y%2F29+=+145%2F29+ ALIGN=MIDDLE  ALT=\"+29y%2F29+=+145%2F29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+145%2F29+ ALIGN=MIDDLE  ALT=\"+y+=+145%2F29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+5+ ALIGN=MIDDLE  ALT=\"+y+=+5+\"   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=+y+=+5+ ALIGN=MIDDLE  ALT=\"+y+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now replace \"y\" with \"5\" in one of the original 2 system equations<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%283x%2B+2y+=4%2C+5x+%2B+13y++=+55%29+ ALIGN=MIDDLE  ALT=\"+system+%283x%2B+2y+=4%2C+5x+%2B+13y++=+55%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "we will use the first equation<BR>\n" );
document.write( ".<BR>\n" );
document.write( "replace \"y\" with \"5\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+2y+=+4+ ALIGN=MIDDLE  ALT=\"+3x+%2B+2y+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+2%285%29+=+4+ ALIGN=MIDDLE  ALT=\"+3x+%2B+2%285%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+10+=+4+ ALIGN=MIDDLE  ALT=\"+3x+%2B+10+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now we will move \"10\" to the rights side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+10+=+4+ ALIGN=MIDDLE  ALT=\"+3x+%2B+10+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+10+-+10+=+4+-+10+ ALIGN=MIDDLE  ALT=\"+3x+%2B+10+-+10+=+4+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+=+%28-6%29+ ALIGN=MIDDLE  ALT=\"+3x+=+%28-6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "To find \"x\" we can divide 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+=+%28-6%29+ ALIGN=MIDDLE  ALT=\"+3x+=+%28-6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%2F3+=+%28-6%29%2F3+ ALIGN=MIDDLE  ALT=\"+3x%2F3+=+%28-6%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-6%29%2F3+ ALIGN=MIDDLE  ALT=\"+x+=+%28-6%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-2%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-2%29+\"   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+=+%28-2%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-2%29+\"   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=+y+=+5+ ALIGN=MIDDLE  ALT=\"+y+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "We can check our two answers by replacing \"x\" and \"y\" with the numbers in the other 2 system equation<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x+%2B+13y++=+55+ ALIGN=MIDDLE  ALT=\"+5x+%2B+13y++=+55+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%28-2%29+%2B+13%285%29++=+55+ ALIGN=MIDDLE  ALT=\"+5%28-2%29+%2B+13%285%29++=+55+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-10%29+%2B+65++=+55+ ALIGN=MIDDLE  ALT=\"+%28-10%29+%2B+65++=+55+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+55++=+55+ ALIGN=MIDDLE  ALT=\"+55++=+55+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( True )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now all we need to do is find \"z\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We need to use one of the three original equations<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system+%283x%2B4y%2Bz=7%2C+2y%2Bz=3%2C+-5x%2B3y%2B8z=-31+%29+ ALIGN=MIDDLE  ALT=\"+system+%283x%2B4y%2Bz=7%2C+2y%2Bz=3%2C+-5x%2B3y%2B8z=-31+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "We will use the second equation<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-2%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-2%29+\"   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=+y+=+5+ ALIGN=MIDDLE  ALT=\"+y+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Replace the letters<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y%2Bz=3+ ALIGN=MIDDLE  ALT=\"+2y%2Bz=3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%285%29%2Bz=3+ ALIGN=MIDDLE  ALT=\"+2%285%29%2Bz=3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2Bz=3+ ALIGN=MIDDLE  ALT=\"+10%2Bz=3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will move \"10\" to the right side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2Bz=3+ ALIGN=MIDDLE  ALT=\"+10%2Bz=3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10+-+10+%2Bz=3+-+10+ ALIGN=MIDDLE  ALT=\"+10+-+10+%2Bz=3+-+10+\"   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=+z=+%28-7%29+ ALIGN=MIDDLE  ALT=\"+z=+%28-7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "We can check our answers by replacing \"x\",\"y\", and \"z\" in the other two equations<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-2%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-2%29+\"   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=+y+=+5+ ALIGN=MIDDLE  ALT=\"+y+=+5+\"   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=+z=+%28-7%29+ ALIGN=MIDDLE  ALT=\"+z=+%28-7%29+\"   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=+system+%283x%2B4y%2Bz=7%2C+-5x%2B3y%2B8z=-31+%29+ ALIGN=MIDDLE  ALT=\"+system+%283x%2B4y%2Bz=7%2C+-5x%2B3y%2B8z=-31+%29+\"   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%2B4y%2Bz=7+ ALIGN=MIDDLE  ALT=\"+3x%2B4y%2Bz=7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%28-2%29%2B4%285%29%2B%28-7%29=7+ ALIGN=MIDDLE  ALT=\"+3%28-2%29%2B4%285%29%2B%28-7%29=7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-6%29%2B20+-+7=7+ ALIGN=MIDDLE  ALT=\"+%28-6%29%2B20+-+7=7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7+=+7+ ALIGN=MIDDLE  ALT=\"+7+=+7+\"   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=+-5x%2B3y%2B8z=-31+ ALIGN=MIDDLE  ALT=\"+-5x%2B3y%2B8z=-31+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5%28-2%29%2B3%285%29%2B8%28-7%29=-31+ ALIGN=MIDDLE  ALT=\"+-5%28-2%29%2B3%285%29%2B8%28-7%29=-31+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2B15+-+56+=-31+ ALIGN=MIDDLE  ALT=\"+10%2B15+-+56+=-31+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-31+=+-31+ ALIGN=MIDDLE  ALT=\"+-31+=+-31+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( True )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "These answers are given in the ordered pair ( x,y,z ), our ordered pair/answer is (-2 , 5 , -7 )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope I helped, Levi </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );