document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127011>Question 127011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you solve each system by substitution?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93016 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find a constant value or values that you can multiply one or both equations by so that you will result in the coefficients on one of the variables having coefficients that are additive inverses.  Then add the two equations together, term by term, and the result will be the elimination of one of the variables.\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=4 ALIGN=MIDDLE  ALT=\"2x-y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-y=6 ALIGN=MIDDLE  ALT=\"3x-y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You could multiply the first equation by -1 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By=-4 ALIGN=MIDDLE  ALT=\"-2x%2By=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > that way when you add the two equations together you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x+%2B+0y+=+2 ALIGN=MIDDLE  ALT=\"1x+%2B+0y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then knowing what x is, you can substitute that back into either of the equations and easily compute y.\r<BR>\n" );
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document.write( "Or, you could multiply the first equation by 3 and the second equation by -2, giving you:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-3y=12 ALIGN=MIDDLE  ALT=\"6x-3y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B2y=-12 ALIGN=MIDDLE  ALT=\"-6x%2B2y=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Adding gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x+-+1y+=+0 ALIGN=MIDDLE  ALT=\"0x+-+1y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and then you can substitute this value for y to easily compute x.\r<BR>\n" );
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