document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145410>Question 145410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone tell me if I got this systems of equations problem right? This one is solved using the substitution method.\r<BR>\n" );
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document.write( "-3x + y = -4<BR>\n" );
document.write( "  x - y = 0\r<BR>\n" );
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document.write( "I got (2,2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106083 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=106083\">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%28-3x%2By=-4%2Cx-y=0%29 ALIGN=MIDDLE  ALT=\"system%28-3x%2By=-4%2Cx-y=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.\r<BR>\n" );
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document.write( "So let's isolate y in the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2By=-4 ALIGN=MIDDLE  ALT=\"-3x%2By=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4%2B3x ALIGN=MIDDLE  ALT=\"y=-4%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2B3x-4 ALIGN=MIDDLE  ALT=\"y=%2B3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-4 ALIGN=MIDDLE  ALT=\"y=3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can now replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the second equation with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-4 ALIGN=MIDDLE  ALT=\"3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for <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-highlight%28%283x-4%29%29=0 ALIGN=MIDDLE  ALT=\"x-highlight%28%283x-4%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-4 ALIGN=MIDDLE  ALT=\"y=3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation. In other words, replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-4 ALIGN=MIDDLE  ALT=\"3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice we've eliminated the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > variables. So we now have a simple equation with one unknown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3x%2B4=0 ALIGN=MIDDLE  ALT=\"x-3x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the negative\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2B4=0 ALIGN=MIDDLE  ALT=\"-2x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x=0-4 ALIGN=MIDDLE  ALT=\"-2x=0-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 4 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x=-4 ALIGN=MIDDLE  ALT=\"-2x=-4\"   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=%28-4%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"x=%28-4%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -2 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "-----------------First Answer------------------------------\r<BR>\n" );
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document.write( "So the first part of our answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can plug it into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-4 ALIGN=MIDDLE  ALT=\"y=3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember we previously solved for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the first equation).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-4 ALIGN=MIDDLE  ALT=\"y=3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the equation where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > was previously isolated.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%282%29-4 ALIGN=MIDDLE  ALT=\"y=3%282%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   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=6-4 ALIGN=MIDDLE  ALT=\"y=6-4\"   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=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms \r<BR>\n" );
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document.write( "-----------------Second Answer------------------------------\r<BR>\n" );
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document.write( "So the second part of our answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------------Summary------------------------------\r<BR>\n" );
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document.write( "So our answers are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which form the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(2,2\right)\"> \r<BR>\n" );
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document.write( "Now let's graph the two equations (if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)\r<BR>\n" );
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document.write( "From the graph, we can see that the two equations intersect at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(2,2\right)\">. 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=%0D%0Adrawing%28500%2C+500%2C+-10%2C10%2C-10%2C10%2C%0D%0A++graph%28500%2C+500%2C+-10%2C10%2C-10%2C10%2C+%28-4--3%2Ax%29%2F%281%29%2C+%280-1%2Ax%29%2F%28-1%29+%29%2C%0D%0A++blue%28circle%282%2C2%2C0.1%29%29%2C%0D%0A++blue%28circle%282%2C2%2C0.12%29%29%2C%0D%0A++blue%28circle%282%2C2%2C0.15%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2By=-4 ALIGN=MIDDLE  ALT=\"-3x%2By=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=0 ALIGN=MIDDLE  ALT=\"x-y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green)  and the intersection of the lines (blue circle).\r<BR>\n" );
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