document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106122>Question 106122</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495108510/algebrahomeworkh>Elementary and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following systems by graphing:\r<BR>\n" );
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document.write( "2x-3y = 12<BR>\n" );
document.write( "-2x+y -8\r<BR>\n" );
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document.write( "I finished the problem and then checked my answer in the back of the book. I got the first one correct but cannot figure out the second part. \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77203 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y+=+12 ALIGN=MIDDLE  ALT=\"2x-3y+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By+-8 ALIGN=MIDDLE  ALT=\"-2x%2By+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By+=+8 ALIGN=MIDDLE  ALT=\"-2x%2By+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_by_graphing.solver>Solve the System of Equations by Graphing</A></TD></TR>\n" );
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document.write( "  Start with the given system of equations:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=12 ALIGN=MIDDLE  ALT=\"2x-3y=12\"   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=-2x%2By=8 ALIGN=MIDDLE  ALT=\"-2x%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  In order to graph these equations, we need to solve for y for each equation.<BR>\n" );
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document.write( "  So let's solve for y on the first equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=12 ALIGN=MIDDLE  ALT=\"2x-3y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y=12-2x ALIGN=MIDDLE  ALT=\"-3y=12-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+x ALIGN=MIDDLE  ALT=\"2+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y=-2x%2B12 ALIGN=MIDDLE  ALT=\"-3y=-2x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2x%2B12%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"y=%28-2x%2B12%29%2F%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-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=y=%28-2%2F-3%29x%2B%2812%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"y=%28-2%2F-3%29x%2B%2812%29%2F%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x-4 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  Now lets graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x-4 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%282%2F3%29x-4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%282%2F3%29x-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x-4 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So let's solve for y on the second equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By=8 ALIGN=MIDDLE  ALT=\"-2x%2By=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y=8%2B2x ALIGN=MIDDLE  ALT=\"1y=8%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+x ALIGN=MIDDLE  ALT=\"2+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y=%2B2x%2B8 ALIGN=MIDDLE  ALT=\"1y=%2B2x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%2B2x%2B8%29%2F%281%29 ALIGN=MIDDLE  ALT=\"y=%28%2B2x%2B8%29%2F%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   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=%28%2B2%2F1%29x%2B%288%29%2F%281%29 ALIGN=MIDDLE  ALT=\"y=%28%2B2%2F1%29x%2B%288%29%2F%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B8 ALIGN=MIDDLE  ALT=\"y=2x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  Now lets add the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B8 ALIGN=MIDDLE  ALT=\"y=2x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to our first plot to get:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%282%2F3%29x-4%2C2x%2B8%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%282%2F3%29x-4%2C2x%2B8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x-4 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >(red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B8 ALIGN=MIDDLE  ALT=\"y=2x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >(green)<BR>\n" );
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document.write( "  From the graph, we can see that the two lines intersect at the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10 ALIGN=MIDDLE  ALT=\"-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >) (note: you might have to adjust the window to see the intersection)</TD></TR>\n" );
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