document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=724359>Question 724359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation using substitution<BR>\n" );
document.write( "3y=x+6<BR>\n" );
document.write( "x=2y-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443717 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=443717\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Substitution means getting one of the equations to a form like<BR>\n" );
document.write( "x = expression that does not include x<BR>\n" );
document.write( "or<BR>\n" );
document.write( "y = expression that does not include y,<BR>\n" );
document.write( "and substituting the expression for the variable in the other equation.<BR>\n" );
document.write( " <BR>\n" );
document.write( "In the case of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283y=x%2B6%2Cx=2y-2%29 ALIGN=MIDDLE  ALT=\"system%283y=x%2B6%2Cx=2y-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y-2 ALIGN=MIDDLE  ALT=\"x=2y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "already is in the form we want.<BR>\n" );
document.write( "It says that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to <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;\" > .<BR>\n" );
document.write( "So we substitute the expression <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;\" > 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;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=x%2B6 ALIGN=MIDDLE  ALT=\"3y=x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=2y-2%2B6 ALIGN=MIDDLE  ALT=\"3y=2y-2%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=2y%2B4 ALIGN=MIDDLE  ALT=\"3y=2y%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y-2y=2y%2B4-2y ALIGN=MIDDLE  ALT=\"3y-2y=2y%2B4-2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=4%29 ALIGN=MIDDLE  ALT=\"highlight%28y=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Now we got back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y-2 ALIGN=MIDDLE  ALT=\"x=2y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and plug <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;\" > into it to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%284%29-2 ALIGN=MIDDLE  ALT=\"x=2%284%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4-2 ALIGN=MIDDLE  ALT=\"x=4-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=6%29 ALIGN=MIDDLE  ALT=\"highlight%28x=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTES:<BR>\n" );
document.write( "If none of the equation was in such a friendly form, we could convert it into the form we want.<BR>\n" );
document.write( "For example, if we had <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283y=x%2B6%2C+4x%2B3y=21%29 ALIGN=MIDDLE  ALT=\"system%283y=x%2B6%2C+4x%2B3y=21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "we would 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;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=x%2B6 ALIGN=MIDDLE  ALT=\"3y=x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the x is not multiplied by anything other than 1, and that makes it easy.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=x%2B6 ALIGN=MIDDLE  ALT=\"3y=x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y-6=x%2B6-6 ALIGN=MIDDLE  ALT=\"3y-6=x%2B6-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y-6=x ALIGN=MIDDLE  ALT=\"3y-6=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3y-6 ALIGN=MIDDLE  ALT=\"x=3y-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If all the coefficients in front of x or y are number other than the usually omitted 1 and -1, solving for a variable gets ugly and we end up with fractions. In those cases, substitution may not be a good choice. </SPAN>\n" );
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