document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=397332>Question 397332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the intersection of the line through the points (7,10) and (4,2) with the line y=x. The point of intersection is (A,B) where A=? and B=? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #281640 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=281640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x1=+7 ALIGN=MIDDLE  ALT=\"x1=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y1=+10 ALIGN=MIDDLE  ALT=\"+y1=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x2=+4+ ALIGN=MIDDLE  ALT=\"+x2=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y2=+2 ALIGN=MIDDLE  ALT=\"y2=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solpe <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=+%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"m=+%28y2-y1%29%2F%28x2-x1%29\"   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=%282-%2810%29%29%2F%284-%287%29%29 ALIGN=MIDDLE  ALT=\"%282-%2810%29%29%2F%284-%287%29%29\"   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=%282-10%29%2F%284-7%29 ALIGN=MIDDLE  ALT=\"%282-10%29%2F%284-7%29\"   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=-8%2F-3 ALIGN=MIDDLE  ALT=\"-8%2F-3\"   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=8%2F3 ALIGN=MIDDLE  ALT=\"8%2F3\"   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=b+=+%28y1-m%2Ax1%29 ALIGN=MIDDLE  ALT=\"b+=+%28y1-m%2Ax1%29\"   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=b+=10-%28%28-8%29%2F%28-3%29%29%287%29+=+10-+%2856%2F3%29+=+-26%2F3 ALIGN=MIDDLE  ALT=\"b+=10-%28%28-8%29%2F%28-3%29%29%287%29+=+10-+%2856%2F3%29+=+-26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+mx+%2Bb+ ALIGN=MIDDLE  ALT=\"y=+mx+%2Bb+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+slope ALIGN=MIDDLE  ALT=\"m+=+slope\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equation of the line is :\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%288%2F3%29+x+-26%2F3 ALIGN=MIDDLE  ALT=\"y+=+%288%2F3%29+x+-26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----(1)\r<BR>\n" );
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document.write( "To find the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=intersection ALIGN=MIDDLE  ALT=\"intersection\"   DISABLED_style= \"max-width:90%; height:auto;\" > of this line with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x ALIGN=MIDDLE  ALT=\"y=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y ALIGN=MIDDLE  ALT=\"+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in (1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288%2F3%29x+-+26%2F3 ALIGN=MIDDLE  ALT=\"x+=+%288%2F3%29x+-+26%2F3\"   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=3x=8x-26 ALIGN=MIDDLE  ALT=\"3x=8x-26\"   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=-5x=-26 ALIGN=MIDDLE  ALT=\"-5x=-26\"   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=x=26%2F5 ALIGN=MIDDLE  ALT=\"x=26%2F5\"   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=y=%288%2F3%29%2826%2F5%29-26%2F3 ALIGN=MIDDLE  ALT=\"y=%288%2F3%29%2826%2F5%29-26%2F3\"   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=y=208%2F15+-26%2F3 ALIGN=MIDDLE  ALT=\"y=208%2F15+-26%2F3\"   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=y=78%2F15+=+26%2F5=5%281%2F5%29 ALIGN=MIDDLE  ALT=\"y=78%2F15+=+26%2F5=5%281%2F5%29\"   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=A=5%281%2F5%29 ALIGN=MIDDLE  ALT=\"A=5%281%2F5%29\"   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=B=5%281%2F5%29 ALIGN=MIDDLE  ALT=\"B=5%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "graph:\r<BR>\n" );
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document.write( "in standard form you have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F3%29+x+-+y+=+26%2F3+ ALIGN=MIDDLE  ALT=\"%288%2F3%29+x+-+y+=+26%2F3+\"   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=y=x ALIGN=MIDDLE  ALT=\"y=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >...or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=0 ALIGN=MIDDLE  ALT=\"x-y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\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( "  <BR>\n" );
document.write( "  Let's look at the first equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F3%29x-y=26%2F3 ALIGN=MIDDLE  ALT=\"%288%2F3%29x-y=26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%288%2F3%29x-y%29=3%2826%2F3%29 ALIGN=MIDDLE  ALT=\"3%28%288%2F3%29x-y%29=3%2826%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides of the first equation by the LCD 3<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x-3y=26 ALIGN=MIDDLE  ALT=\"8x-3y=26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute<BR>\n" );
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document.write( "  ---------<BR>\n" );
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document.write( "  So our new system of equations is:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x-3y=26 ALIGN=MIDDLE  ALT=\"8x-3y=26\"   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=1x-y=0 ALIGN=MIDDLE  ALT=\"1x-y=0\"   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=8x-3y=26 ALIGN=MIDDLE  ALT=\"8x-3y=26\"   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=26-8x ALIGN=MIDDLE  ALT=\"-3y=26-8x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+x ALIGN=MIDDLE  ALT=\"8+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=-8x%2B26 ALIGN=MIDDLE  ALT=\"-3y=-8x%2B26\"   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=%28-8x%2B26%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"y=%28-8x%2B26%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=%28-8%2F-3%29x%2B%2826%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"y=%28-8%2F-3%29x%2B%2826%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=%288%2F3%29x-26%2F3 ALIGN=MIDDLE  ALT=\"y=%288%2F3%29x-26%2F3\"   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=%288%2F3%29x-26%2F3 ALIGN=MIDDLE  ALT=\"y=%288%2F3%29x-26%2F3\"   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+%288%2F3%29x-26%2F3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%288%2F3%29x-26%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%288%2F3%29x-26%2F3 ALIGN=MIDDLE  ALT=\"y=%288%2F3%29x-26%2F3\"   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=1x-y=0 ALIGN=MIDDLE  ALT=\"1x-y=0\"   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=-y=0-x ALIGN=MIDDLE  ALT=\"-y=0-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x ALIGN=MIDDLE  ALT=\"+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=-y=-x%2B0 ALIGN=MIDDLE  ALT=\"-y=-x%2B0\"   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-x%2B0%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"y=%28-x%2B0%29%2F%28-1%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=%28-1%2F-1%29x%2B%280%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"y=%28-1%2F-1%29x%2B%280%29%2F%28-1%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=x%2B0 ALIGN=MIDDLE  ALT=\"y=x%2B0\"   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=x%2B0 ALIGN=MIDDLE  ALT=\"y=x%2B0\"   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+%288%2F3%29x-26%2F3%2Cx%2B0%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%288%2F3%29x-26%2F3%2Cx%2B0%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%288%2F3%29x-26%2F3 ALIGN=MIDDLE  ALT=\"y=%288%2F3%29x-26%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B0 ALIGN=MIDDLE  ALT=\"y=x%2B0\"   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=26%2F5 ALIGN=MIDDLE  ALT=\"26%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%2F5 ALIGN=MIDDLE  ALT=\"26%2F5\"   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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document.write( "\n" );
document.write( " </SPAN>\n" );
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