document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218289>Question 218289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to know if my answer is correct for the following:  If it isn't, I need to know why. thanks<BR>\n" );
document.write( "Solve the system of equations<BR>\n" );
document.write( "x+2y=1<BR>\n" );
document.write( "3x-2y=11<BR>\n" );
document.write( "My answer is (3,-1)<BR>\n" );
document.write( "Thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164447 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=164447\">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%28x%2B2y=1%2C3x-2y=11%29 ALIGN=MIDDLE  ALT=\"system%28x%2B2y=1%2C3x-2y=11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "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=%28x%2B2y%29%2B%283x-2y%29=%281%29%2B%2811%29 ALIGN=MIDDLE  ALT=\"%28x%2B2y%29%2B%283x-2y%29=%281%29%2B%2811%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=%281x%2B3x%29%2B%282y%2B-2y%29=1%2B11 ALIGN=MIDDLE  ALT=\"%281x%2B3x%29%2B%282y%2B-2y%29=1%2B11\"   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=4x%2B0y=12 ALIGN=MIDDLE  ALT=\"4x%2B0y=12\"   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=4x=12 ALIGN=MIDDLE  ALT=\"4x=12\"   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=%2812%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%2812%29%2F%284%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=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=x%2B2y=1 ALIGN=MIDDLE  ALT=\"x%2B2y=1\"   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=3%2B2y=1 ALIGN=MIDDLE  ALT=\"3%2B2y=1\"   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=3%2B2y=1 ALIGN=MIDDLE  ALT=\"3%2B2y=1\"   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=2y=1-3 ALIGN=MIDDLE  ALT=\"2y=1-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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=2y=-2 ALIGN=MIDDLE  ALT=\"2y=-2\"   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=%28-2%29%2F%282%29 ALIGN=MIDDLE  ALT=\"y=%28-2%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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 our answer is <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)\">. Good job. As a check, simply 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;\" > 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;\" > and you should get two identities.\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%281-x%29%2F%282%29%2C%2811-3x%29%2F%28-2%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=x%2B2y=1 ALIGN=MIDDLE  ALT=\"x%2B2y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=11 ALIGN=MIDDLE  ALT=\"3x-2y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) \r<BR>\n" );
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document.write( " </SPAN>\n" );
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