document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199100>Question 199100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve algebraically and check:<BR>\n" );
document.write( "         2x+4y=2<BR>\n" );
document.write( "         3x-6y=15 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149562 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=149562\">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%282x%2B4y=2%2C3x-6y=15%29 ALIGN=MIDDLE  ALT=\"system%282x%2B4y=2%2C3x-6y=15%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%2B4y%29=3%282%29 ALIGN=MIDDLE  ALT=\"3%282x%2B4y%29=3%282%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%2B12y=6 ALIGN=MIDDLE  ALT=\"6x%2B12y=6\"   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=2%283x-6y%29=2%2815%29 ALIGN=MIDDLE  ALT=\"2%283x-6y%29=2%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the second equation by 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-12y=30 ALIGN=MIDDLE  ALT=\"6x-12y=30\"   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%2B12y=6%2C6x-12y=30%29 ALIGN=MIDDLE  ALT=\"system%286x%2B12y=6%2C6x-12y=30%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%2B12y%29%2B%286x-12y%29=%286%29%2B%2830%29 ALIGN=MIDDLE  ALT=\"%286x%2B12y%29%2B%286x-12y%29=%286%29%2B%2830%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%2B6x%29%2B%2812y%2B-12y%29=6%2B30 ALIGN=MIDDLE  ALT=\"%286x%2B6x%29%2B%2812y%2B-12y%29=6%2B30\"   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=12x%2B0y=36 ALIGN=MIDDLE  ALT=\"12x%2B0y=36\"   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=12x=36 ALIGN=MIDDLE  ALT=\"12x=36\"   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=%2836%29%2F%2812%29 ALIGN=MIDDLE  ALT=\"x=%2836%29%2F%2812%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=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=3 ALIGN=MIDDLE  ALT=\"x=3\"   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%2B12y=6 ALIGN=MIDDLE  ALT=\"6x%2B12y=6\"   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%283%29%2B12y=6 ALIGN=MIDDLE  ALT=\"6%283%29%2B12y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=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=18%2B12y=6 ALIGN=MIDDLE  ALT=\"18%2B12y=6\"   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=6-18 ALIGN=MIDDLE  ALT=\"12y=6-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   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=-12 ALIGN=MIDDLE  ALT=\"12y=-12\"   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=%28-12%29%2F%2812%29 ALIGN=MIDDLE  ALT=\"y=%28-12%29%2F%2812%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=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   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=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   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(3,-1\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(3,-1\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-7%2C13%2C-11%2C9%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28500%2C500%2C-7%2C13%2C-11%2C9%2C%282-2x%29%2F%284%29%2C%2815-3x%29%2F%28-6%29%29%2C%0D%0Acircle%283%2C-1%2C0.05%29%2C%0D%0Acircle%283%2C-1%2C0.08%29%2C%0D%0Acircle%283%2C-1%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%2B4y=2 ALIGN=MIDDLE  ALT=\"2x%2B4y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-6y=15 ALIGN=MIDDLE  ALT=\"3x-6y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) \r<BR>\n" );
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document.write( "I'll let you do the check. </SPAN>\n" );
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