document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170002>Question 170002</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Solve by substitution or elimination method: <BR>\n" );
document.write( "             3x -  2y = 8<BR>\n" );
document.write( "             -12x + 8y = 32<BR>\n" );
document.write( " Solve by substitution or elimination method: <BR>\n" );
document.write( "        7x - 5y = 14<BR>\n" );
document.write( "             -4x + y = 27<BR>\n" );
document.write( " Solve by substitution or elimination method: <BR>\n" );
document.write( "             -4x + 3y = 5<BR>\n" );
document.write( "              12x - 9y = -15<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125471 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=125471\">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 by substitution or elimination method:<BR>\n" );
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document.write( "3x - 2y = 8<BR>\n" );
document.write( "-12x + 8y = 32<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve by substitution or elimination method:<BR>\n" );
document.write( ". <BR>\n" );
document.write( "7x - 5y = 14<BR>\n" );
document.write( "-4x + y = 27<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve by substitution or elimination method:<BR>\n" );
document.write( ". <BR>\n" );
document.write( "-4x + 3y = 5<BR>\n" );
document.write( "12x - 9y = -15<BR>\n" );
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document.write( "First we will solve the first system with substitution<BR>\n" );
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document.write( "3x - 2y = 8<BR>\n" );
document.write( "-12x + 8y = 32<BR>\n" );
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document.write( "First we need to solve for a variable in one of the two equations, doesn't matter which letter, or equation, we will solve for \"y\" in the first equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+2y+=+8+ ALIGN=MIDDLE  ALT=\"+3x+-+2y+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 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=+3x+-+2y+=+8+ ALIGN=MIDDLE  ALT=\"+3x+-+2y+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+2y+%2B+2y+=+8+%2B+2y+ ALIGN=MIDDLE  ALT=\"+3x+-+2y+%2B+2y+=+8+%2B+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+=+8+%2B+2y+ ALIGN=MIDDLE  ALT=\"+3x+=+8+%2B+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we need to move \"8\" to the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+=+8+%2B+2y+ ALIGN=MIDDLE  ALT=\"+3x+=+8+%2B+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+8+=+8+-+8+%2B+2y+ ALIGN=MIDDLE  ALT=\"+3x+-+8+=+8+-+8+%2B+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+8+=+2y+ ALIGN=MIDDLE  ALT=\"+3x+-+8+=+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to find \"y\" we need to 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=+3x+-+8+=+2y+ ALIGN=MIDDLE  ALT=\"+3x+-+8+=+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283x+-+8%29%2F2+=+2y%2F2+ ALIGN=MIDDLE  ALT=\"+%283x+-+8%29%2F2+=+2y%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283x+-+8%29%2F2+=+y+ ALIGN=MIDDLE  ALT=\"+%283x+-+8%29%2F2+=+y+\"   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=+y+=+%283x+-+8%29%2F2+ ALIGN=MIDDLE  ALT=\"+y+=+%283x+-+8%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since \"y\" is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283x+-+8%29%2F2+ ALIGN=MIDDLE  ALT=\"+%283x+-+8%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can replace \"y\" in the other equation with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283x+-+8%29%2F2+ ALIGN=MIDDLE  ALT=\"+%283x+-+8%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then just solve for \"x\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12x+%2B+8y+=+32+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+8y+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12x+%2B+8%28%283x+-+8%29%2F2%29+=+32+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+8%28%283x+-+8%29%2F2%29+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now just solve for \"x\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12x+%2B+8%28%283x+-+8%29%2F2%29+=+32+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+8%28%283x+-+8%29%2F2%29+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12x+%2B+4%28%283x+-+8%29%2F1%29+=+32+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+4%28%283x+-+8%29%2F1%29+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12x+%2B+4%283x+-+8%29+=+32+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+4%283x+-+8%29+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now 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=+-12x+%2B+highlight%284%29%28highlight%283x%29+-+8%29+=+32+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+highlight%284%29%28highlight%283x%29+-+8%29+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12x+%2B+highlight%284%29%283x+-+highlight%288%29%29+=+32+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+highlight%284%29%283x+-+highlight%288%29%29+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Remember the + and - signs,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12x+%2B+12x+-+32+=+32+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+12x+-+32+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, adding the \"x\"'s<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12x+%2B+12x+-+32+=+32+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+12x+-+32+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0x+-+32+=+32+ ALIGN=MIDDLE  ALT=\"+0x+-+32+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-+32+=+32+ ALIGN=MIDDLE  ALT=\"+-+32+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( False )<BR>\n" );
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document.write( "This means ( when the x's or y's cancel out, and there is a false statement) that there are no solutions, these lines are parallel, there is no intersection, and therefore no solutions<BR>\n" );
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document.write( "Here is the graph of this system<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph+%28+300%2C300%2C-10%2C10%2C-10%2C10%2C+%283x+-+8%29%2F2%2C+%283x%2B8%29%2F2+%29+ ALIGN=MIDDLE  ALT=\"+graph+%28+300%2C300%2C-10%2C10%2C-10%2C10%2C+%283x+-+8%29%2F2%2C+%283x%2B8%29%2F2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we will solve the second system, by elimination<BR>\n" );
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document.write( "7x - 5y = 14<BR>\n" );
document.write( "-4x + y = 27<BR>\n" );
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document.write( "Elimination is when you add the two equations together, and it gets rid of a variable, first we need to make sure the x's or y's in each equation are the same, or the negative of the other<BR>\n" );
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document.write( "We can eliminate any variable ( either x or y )<BR>\n" );
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document.write( "We will get rid of the y's<BR>\n" );
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document.write( "We need to either get both y's to \"5y\" or \"-5y\" or we need to get them to \"y\" or \"-y\", we will change the second equation to \"5y\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4x+%2B+y+=+27+ ALIGN=MIDDLE  ALT=\"+-4x+%2B+y+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to get \"y\" to change to \"5y\" we need to multiply each side by (5)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4x+%2B+y+=+27+ ALIGN=MIDDLE  ALT=\"+-4x+%2B+y+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%28-4x+%2B+y%29+=+5%2827%29+ ALIGN=MIDDLE  ALT=\"+5%28-4x+%2B+y%29+=+5%2827%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%28-4x+%2B+y%29+=+135+ ALIGN=MIDDLE  ALT=\"+5%28-4x+%2B+y%29+=+135+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will need to use the distribution method<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%28-4x+%2B+y%29+=+135+ ALIGN=MIDDLE  ALT=\"+5%28-4x+%2B+y%29+=+135+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%285%29%28highlight%28-4x%29+%2B+y%29+=+135+ ALIGN=MIDDLE  ALT=\"+highlight%285%29%28highlight%28-4x%29+%2B+y%29+=+135+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%285%29%28-4x+%2B+highlight%28y%29%29+=+135+ ALIGN=MIDDLE  ALT=\"+highlight%285%29%28-4x+%2B+highlight%28y%29%29+=+135+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Remember the signs, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-20x+%2B+5y+=+135+ ALIGN=MIDDLE  ALT=\"+-20x+%2B+5y+=+135+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is our new equation<BR>\n" );
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document.write( "Now we will bring the firt equation to our second new equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7x+-+5y+=+14+ ALIGN=MIDDLE  ALT=\"+7x+-+5y+=+14+\"   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=+-20x+%2B+5y+=+135+ ALIGN=MIDDLE  ALT=\"+-20x+%2B+5y+=+135+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will now add the equations<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7x+-+5y+=+14+ ALIGN=MIDDLE  ALT=\"+7x+-+5y+=+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=+-20x+%2B+5y+=+135+ ALIGN=MIDDLE  ALT=\"+-20x+%2B+5y+=+135+\"   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=+7x+%2B+%28-20x%29+ ALIGN=MIDDLE  ALT=\"+7x+%2B+%28-20x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-13x+ ALIGN=MIDDLE  ALT=\"+-13x+\"   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=+-5y+%2B+5y+ ALIGN=MIDDLE  ALT=\"+-5y+%2B+5y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0y+ ALIGN=MIDDLE  ALT=\"+0y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   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=+14+%2B+135+ ALIGN=MIDDLE  ALT=\"+14+%2B+135+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=149 ALIGN=MIDDLE  ALT=\"149\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "It will become <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-13x+%2B+0+=+149+ ALIGN=MIDDLE  ALT=\"+-13x+%2B+0+=+149+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-13x+=+149+ ALIGN=MIDDLE  ALT=\"+-13x+=+149+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to find \"x\" we need to divide each side by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-13+ ALIGN=MIDDLE  ALT=\"+-13+\"   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=+-13x+=+149+ ALIGN=MIDDLE  ALT=\"+-13x+=+149+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-13x%2F-13+=+149%2F-13+ ALIGN=MIDDLE  ALT=\"+-13x%2F-13+=+149%2F-13+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+149%2F-13+ ALIGN=MIDDLE  ALT=\"+x+=+149%2F-13+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-149%2F13+ ALIGN=MIDDLE  ALT=\"+x+=+-149%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can now replace \"x\" with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-149%2F13+ ALIGN=MIDDLE  ALT=\"++-149%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, in one of the two original equations<BR>\n" );
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document.write( "7x - 5y = 14<BR>\n" );
document.write( "-4x + y = 27<BR>\n" );
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document.write( "We will use the second equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4x+%2B+y+=+27+ ALIGN=MIDDLE  ALT=\"+-4x+%2B+y+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4%28-149%2F13%29+%2B+y+=+27+ ALIGN=MIDDLE  ALT=\"+-4%28-149%2F13%29+%2B+y+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-4%2F1%29%28-149%2F13%29+%2B+y+=+27+ ALIGN=MIDDLE  ALT=\"+%28-4%2F1%29%28-149%2F13%29+%2B+y+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28596%2F13%29+%2B+y+=+27+ ALIGN=MIDDLE  ALT=\"+%28596%2F13%29+%2B+y+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we need to move <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+596%2F13+ ALIGN=MIDDLE  ALT=\"+596%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right side ( we will convert \"27\" into \"13ths\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+596%2F13+%2B+y+=+27+ ALIGN=MIDDLE  ALT=\"+596%2F13+%2B+y+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+596%2F13+%2B+y+=+351%2F13+ ALIGN=MIDDLE  ALT=\"+596%2F13+%2B+y+=+351%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28596%2F13%29+-+%28596%2F13%29+%2B+y+=+%28351%2F13%29-%28596%2F13%29+ ALIGN=MIDDLE  ALT=\"+%28596%2F13%29+-+%28596%2F13%29+%2B+y+=+%28351%2F13%29-%28596%2F13%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28351%2F13%29-%28596%2F13%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28351%2F13%29-%28596%2F13%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-245%2F13+ ALIGN=MIDDLE  ALT=\"+y+=+-245%2F13+\"   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+=+-245%2F13+ ALIGN=MIDDLE  ALT=\"+y+=+-245%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can check our answers by replacing \"x\" and \"y\" in both  original equations<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-149%2F13+ ALIGN=MIDDLE  ALT=\"+x+=+-149%2F13+\"   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+=+-245%2F13+ ALIGN=MIDDLE  ALT=\"+y+=+-245%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "First equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7x+-+5y+=+14+ ALIGN=MIDDLE  ALT=\"+7x+-+5y+=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7%28-149%2F13%29+-+5%28-245%2F13%29+=+14+ ALIGN=MIDDLE  ALT=\"+7%28-149%2F13%29+-+5%28-245%2F13%29+=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%287%2F1%29%28-149%2F13%29+-+%28%285%2F1%29%28-245%2F13%29%29+=+14+ ALIGN=MIDDLE  ALT=\"+%287%2F1%29%28-149%2F13%29+-+%28%285%2F1%29%28-245%2F13%29%29+=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-1043%2F13%29+-+%28-1225%2F13%29+=+14+ ALIGN=MIDDLE  ALT=\"+%28-1043%2F13%29+-+%28-1225%2F13%29+=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-1043%2F13%29+%2B+1225%2F13+=+14+ ALIGN=MIDDLE  ALT=\"+%28-1043%2F13%29+%2B+1225%2F13+=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+182%2F13+=+14+ ALIGN=MIDDLE  ALT=\"+182%2F13+=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14+=+14+ ALIGN=MIDDLE  ALT=\"+14+=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( True )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Second equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4x+%2B+y+=+27+ ALIGN=MIDDLE  ALT=\"+-4x+%2B+y+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4%28-149%2F13%29+%2B+%28-245%2F13%29+=+27+ ALIGN=MIDDLE  ALT=\"+-4%28-149%2F13%29+%2B+%28-245%2F13%29+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-4%2F1%29%28-149%2F13%29+-+%28245%2F13%29+=+27+ ALIGN=MIDDLE  ALT=\"+%28-4%2F1%29%28-149%2F13%29+-+%28245%2F13%29+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28596%2F13%29+-+%28245%2F13%29+=+27+ ALIGN=MIDDLE  ALT=\"+%28596%2F13%29+-+%28245%2F13%29+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+351%2F13+=+27+ ALIGN=MIDDLE  ALT=\"+351%2F13+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+27+=+27+ ALIGN=MIDDLE  ALT=\"+27+=+27+\"   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=+x+=+-149%2F13+ ALIGN=MIDDLE  ALT=\"+x+=+-149%2F13+\"   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+=+-245%2F13+ ALIGN=MIDDLE  ALT=\"+y+=+-245%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solution sets are in the form (x,y), our solution set is ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-149%2F13+ ALIGN=MIDDLE  ALT=\"+-149%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-245%2F13+ ALIGN=MIDDLE  ALT=\"+-245%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
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document.write( "The graph of the system is<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing+%28+500%2C500%2C-20%2C20%2C-20%2C20%2Cred+%28circle+%28-149%2F13%2C-245%2F13%2C0.1%29%29%2Cblue+%28circle+%28-149%2F13%2C-245%2F13%2C0.2%29%29%2Cgraph+%28+500%2C500%2C-20%2C20%2C-20%2C20%2C+%287x-14%29%2F5%2C+4x%2B27%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The intersection is your answer<BR>\n" );
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document.write( "Now we can do the last system<BR>\n" );
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document.write( "-4x + 3y = 5<BR>\n" );
document.write( "12x - 9y = -15<BR>\n" );
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document.write( "We will use the elimination method of solving this problem<BR>\n" );
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document.write( "Remember elimination is where you get rid of a variable<BR>\n" );
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document.write( "We will multiply the first equation by \"3\" to get rid of the \"y\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4x+%2B+3y+=+5+ ALIGN=MIDDLE  ALT=\"+-4x+%2B+3y+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%28-4x+%2B+3y%29+=+3%285%29+ ALIGN=MIDDLE  ALT=\"+3%28-4x+%2B+3y%29+=+3%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%28-4x+%2B+3y%29+=+15+ ALIGN=MIDDLE  ALT=\"+3%28-4x+%2B+3y%29+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > we will use distribution<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%28-4x+%2B+3y%29+=+15+ ALIGN=MIDDLE  ALT=\"+3%28-4x+%2B+3y%29+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight+%283%29%28highlight%28-4x%29+%2B+3y%29+=+15+ ALIGN=MIDDLE  ALT=\"+highlight+%283%29%28highlight%28-4x%29+%2B+3y%29+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight+%283%29%28-4x+%2B+highlight%283y%29%29+=+15+ ALIGN=MIDDLE  ALT=\"+highlight+%283%29%28-4x+%2B+highlight%283y%29%29+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Remember signs, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12x+%2B+9y+=+15+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+9y+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we can add the new first equation to the second equation<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12x+%2B+9y+=+15+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+9y+=+15+\"   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=+12x+-+9y+=+-15+ ALIGN=MIDDLE  ALT=\"+12x+-+9y+=+-15+\"   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=+-12x+%2B+12x+ ALIGN=MIDDLE  ALT=\"+-12x+%2B+12x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0x+ ALIGN=MIDDLE  ALT=\"+0x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   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=+9y+%2B+%28-9y%29+ ALIGN=MIDDLE  ALT=\"+9y+%2B+%28-9y%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9y+-+9y+ ALIGN=MIDDLE  ALT=\"+9y+-+9y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0y+ ALIGN=MIDDLE  ALT=\"+0y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   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=+15+%2B+%28-15%29+ ALIGN=MIDDLE  ALT=\"+15+%2B+%28-15%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15+-+15+ ALIGN=MIDDLE  ALT=\"+15+-+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "It will become <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+%2B+0+=+0+ ALIGN=MIDDLE  ALT=\"+0+%2B+0+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+0+ ALIGN=MIDDLE  ALT=\"+0+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "This means ( when both x and y cancel out, and there is a true statement) that this is the same line, both equation will be one line, there is an infinite number of solutions ( since the equations are equal to one line )( or the second line is put on the first line )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Here is the graph of this system<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph+%28+300%2C300%2C+-10%2C10%2C-10%2C10%2C+%284x+%2B+5%29%2F3%2C+%284x%2B5%29%2F3+%29+ ALIGN=MIDDLE  ALT=\"+graph+%28+300%2C300%2C+-10%2C10%2C-10%2C10%2C+%284x+%2B+5%29%2F3%2C+%284x%2B5%29%2F3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Your answers are<BR>\n" );
document.write( ".<BR>\n" );
document.write( "First system of equations = \" no solutions \" ( since they are parallel lines )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Second system of equations = ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-149%2F13+ ALIGN=MIDDLE  ALT=\"+-149%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-245%2F13+ ALIGN=MIDDLE  ALT=\"+-245%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) ( the lines intersect at point ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-149%2F13+ ALIGN=MIDDLE  ALT=\"+-149%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-245%2F13+ ALIGN=MIDDLE  ALT=\"+-245%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Third system of equations = \" infinite solutions \" ( since the two equations are the same line )<BR>\n" );
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document.write( "Hope I helped, Levi\r<BR>\n" );
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document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );