document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=637131>Question 637131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x-4y=40<BR>\n" );
document.write( "8x-3y=82\r<BR>\n" );
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document.write( "Is there no solution for this problem?  I can't come up with anything that works. I need to show work but can't solve it. Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401447 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=401447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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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%282x-4y=40%2C8x-3y=82%29 ALIGN=MIDDLE  ALT=\"system%282x-4y=40%2C8x-3y=82%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=3%282x-4y%29=3%2840%29 ALIGN=MIDDLE  ALT=\"3%282x-4y%29=3%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-12y=120 ALIGN=MIDDLE  ALT=\"6x-12y=120\"   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=-4%288x-3y%29=-4%2882%29 ALIGN=MIDDLE  ALT=\"-4%288x-3y%29=-4%2882%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the second equation by -4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32x%2B12y=-328 ALIGN=MIDDLE  ALT=\"-32x%2B12y=-328\"   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%286x-12y=120%2C-32x%2B12y=-328%29 ALIGN=MIDDLE  ALT=\"system%286x-12y=120%2C-32x%2B12y=-328%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=%286x-12y%29%2B%28-32x%2B12y%29=%28120%29%2B%28-328%29 ALIGN=MIDDLE  ALT=\"%286x-12y%29%2B%28-32x%2B12y%29=%28120%29%2B%28-328%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=%286x%2B-32x%29%2B%28-12y%2B12y%29=120%2B-328 ALIGN=MIDDLE  ALT=\"%286x%2B-32x%29%2B%28-12y%2B12y%29=120%2B-328\"   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=-26x%2B0y=-208 ALIGN=MIDDLE  ALT=\"-26x%2B0y=-208\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-26x=-208 ALIGN=MIDDLE  ALT=\"-26x=-208\"   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=%28-208%29%2F%28-26%29 ALIGN=MIDDLE  ALT=\"x=%28-208%29%2F%28-26%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-26 ALIGN=MIDDLE  ALT=\"-26\"   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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\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=6x-12y=120 ALIGN=MIDDLE  ALT=\"6x-12y=120\"   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=6%288%29-12y=120 ALIGN=MIDDLE  ALT=\"6%288%29-12y=120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=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=48-12y=120 ALIGN=MIDDLE  ALT=\"48-12y=120\"   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=-12y=120-48 ALIGN=MIDDLE  ALT=\"-12y=120-48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   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=-12y=72 ALIGN=MIDDLE  ALT=\"-12y=72\"   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=%2872%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"y=%2872%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   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=-6 ALIGN=MIDDLE  ALT=\"y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\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=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-6 ALIGN=MIDDLE  ALT=\"y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Which form the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(8,-6\right)\">.\r<BR>\n" );
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document.write( "This means that the system is consistent and independent.\r<BR>\n" );
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document.write( "Notice when we graph the equations, we see that they intersect at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(8,-6\right)\">. So this visually verifies our answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-2%2C18%2C-16%2C4%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28500%2C500%2C-2%2C18%2C-16%2C4%2C%2840-2x%29%2F%28-4%29%2C%2882-8x%29%2F%28-3%29%29%2C%0D%0Acircle%288%2C-6%2C0.05%29%2C%0D%0Acircle%288%2C-6%2C0.08%29%2C%0D%0Acircle%288%2C-6%2C0.10%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4y=40 ALIGN=MIDDLE  ALT=\"2x-4y=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x-3y=82 ALIGN=MIDDLE  ALT=\"8x-3y=82\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) <BR>\n" );
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