document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=751292>Question 751292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am stuck on elimination by substitution. The variable has to be \"naked\" or alone, but both x and y have numbers before the variables.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #457105 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=457105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%2BBy=C+ ALIGN=MIDDLE  ALT=\"Ax%2BBy=C+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Dx%2BCy=E ALIGN=MIDDLE  ALT=\"Dx%2BCy=E\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A process to eliminate terms of y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28Ax%2BBy=C%29 ALIGN=MIDDLE  ALT=\"E%28Ax%2BBy=C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%28Dx%2BEy=F%29 ALIGN=MIDDLE  ALT=\"B%28Dx%2BEy=F%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note each entire equation is being multiplied.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AEx%2BBEy=E%2AC ALIGN=MIDDLE  ALT=\"AEx%2BBEy=E%2AC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BDx%2BEBy=B%2AF ALIGN=MIDDLE  ALT=\"BDx%2BEBy=B%2AF\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We may sometimes apply commutative property of multiplication,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AEx%2BBEy=CE ALIGN=MIDDLE  ALT=\"AEx%2BBEy=CE\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BDx%2BBEy=BF ALIGN=MIDDLE  ALT=\"BDx%2BBEy=BF\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract one equation from the other equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AEx%2BBEy-BDx-BEy=CE-BF ALIGN=MIDDLE  ALT=\"AEx%2BBEy-BDx-BEy=CE-BF\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And this is how we have the term, \"elimination method\".\r<BR>\n" );
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document.write( "In this general case, symbolically giving<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AEx-BDx=CE-BF ALIGN=MIDDLE  ALT=\"AEx-BDx=CE-BF\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AE-BD%29x=CE-BF ALIGN=MIDDLE  ALT=\"%28AE-BD%29x=CE-BF\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and then division by the coefficient expression on x,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=%28CE-BF%29%2F%28AE-BD%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x=%28CE-BF%29%2F%28AE-BD%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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