document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175132>Question 175132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5x-2y=37<BR>\n" );
document.write( "3x+4y=9<BR>\n" );
document.write( "It is all one problem setup like above.We have tried to add them together and tried to figure out x and y separately.  This is my student's problem and I thought I would see how it is done step by step and then we can work on the rest of his assigned problems. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130206 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=130206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Start with the given system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%285x-2y=37%2C3x%2B4y=9%29 ALIGN=MIDDLE  ALT=\"system%285x-2y=37%2C3x%2B4y=9%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=2%285x-2y%29=2%2837%29 ALIGN=MIDDLE  ALT=\"2%285x-2y%29=2%2837%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-4y=74 ALIGN=MIDDLE  ALT=\"10x-4y=74\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So we have the new system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2810x-4y=74%2C3x%2B4y=9%29 ALIGN=MIDDLE  ALT=\"system%2810x-4y=74%2C3x%2B4y=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810x-4y%29%2B%283x%2B4y%29=%2874%29%2B%289%29 ALIGN=MIDDLE  ALT=\"%2810x-4y%29%2B%283x%2B4y%29=%2874%29%2B%289%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=%2810x%2B3x%29%2B%28-4y%2B4y%29=74%2B9 ALIGN=MIDDLE  ALT=\"%2810x%2B3x%29%2B%28-4y%2B4y%29=74%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x%2B0y=83 ALIGN=MIDDLE  ALT=\"13x%2B0y=83\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. Notice how the y terms cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x=83 ALIGN=MIDDLE  ALT=\"13x=83\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2883%29%2F%2813%29 ALIGN=MIDDLE  ALT=\"x=%2883%29%2F%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides 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;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "------------------------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-4y=74 ALIGN=MIDDLE  ALT=\"10x-4y=74\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now go back to the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2883%2F13%29-4y=74 ALIGN=MIDDLE  ALT=\"10%2883%2F13%29-4y=74\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=83%2F13 ALIGN=MIDDLE  ALT=\"x=83%2F13\"   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=830%2F13-4y=74 ALIGN=MIDDLE  ALT=\"830%2F13-4y=74\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%28830%2Fcross%2813%29-4y%29=13%2874%29 ALIGN=MIDDLE  ALT=\"13%28830%2Fcross%2813%29-4y%29=13%2874%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear any fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=830-52y=962 ALIGN=MIDDLE  ALT=\"830-52y=962\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-52y=962-830 ALIGN=MIDDLE  ALT=\"-52y=962-830\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=830 ALIGN=MIDDLE  ALT=\"830\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-52y=132 ALIGN=MIDDLE  ALT=\"-52y=132\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28132%29%2F%28-52%29 ALIGN=MIDDLE  ALT=\"y=%28132%29%2F%28-52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-52 ALIGN=MIDDLE  ALT=\"-52\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=-33%2F13 ALIGN=MIDDLE  ALT=\"y=-33%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2883%29%2F%2813%29 ALIGN=MIDDLE  ALT=\"x=%2883%29%2F%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-33%2F13 ALIGN=MIDDLE  ALT=\"y=-33%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "which forms the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{83}{13},-\frac{33}{13}\right)\"> </SPAN>\n" );
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