document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243643>Question 243643</A>: <I><SPAN STYLE=\"word-break: break-all;\">  find the coordinates of -x+3y=12, and 4x+3y=12  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178463 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=178463\">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%28-x%2B3y=12%2C4x%2B3y=12%29 ALIGN=MIDDLE  ALT=\"system%28-x%2B3y=12%2C4x%2B3y=12%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=4%28-x%2B3y%29=4%2812%29 ALIGN=MIDDLE  ALT=\"4%28-x%2B3y%29=4%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%2B12y=48 ALIGN=MIDDLE  ALT=\"-4x%2B12y=48\"   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%28-4x%2B12y=48%2C4x%2B3y=12%29 ALIGN=MIDDLE  ALT=\"system%28-4x%2B12y=48%2C4x%2B3y=12%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=%28-4x%2B12y%29%2B%284x%2B3y%29=%2848%29%2B%2812%29 ALIGN=MIDDLE  ALT=\"%28-4x%2B12y%29%2B%284x%2B3y%29=%2848%29%2B%2812%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=%28-4x%2B4x%29%2B%2812y%2B3y%29=48%2B12 ALIGN=MIDDLE  ALT=\"%28-4x%2B4x%29%2B%2812y%2B3y%29=48%2B12\"   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=0x%2B15y=60 ALIGN=MIDDLE  ALT=\"0x%2B15y=60\"   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=15y=60 ALIGN=MIDDLE  ALT=\"15y=60\"   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=y=%2860%29%2F%2815%29 ALIGN=MIDDLE  ALT=\"y=%2860%29%2F%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   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=4 ALIGN=MIDDLE  ALT=\"y=4\"   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=-4x%2B12y=48 ALIGN=MIDDLE  ALT=\"-4x%2B12y=48\"   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=-4x%2B12%284%29=48 ALIGN=MIDDLE  ALT=\"-4x%2B12%284%29=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   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=-4x%2B48=48 ALIGN=MIDDLE  ALT=\"-4x%2B48=48\"   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=-4x=48-48 ALIGN=MIDDLE  ALT=\"-4x=48-48\"   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=-4x=0 ALIGN=MIDDLE  ALT=\"-4x=0\"   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=x=%280%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x=%280%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   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=0 ALIGN=MIDDLE  ALT=\"x=0\"   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=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   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(0,4\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(0,4\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-10%2C10%2C-6%2C14%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28500%2C500%2C-10%2C10%2C-6%2C14%2C%2812%2Bx%29%2F%283%29%2C%2812-4x%29%2F%283%29%29%2C%0D%0Acircle%280%2C4%2C0.05%29%2C%0D%0Acircle%280%2C4%2C0.08%29%2C%0D%0Acircle%280%2C4%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=-x%2B3y=12 ALIGN=MIDDLE  ALT=\"-x%2B3y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y=12 ALIGN=MIDDLE  ALT=\"4x%2B3y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) <BR>\n" );
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