document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854967>Question 854967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> need to solve the equation using the substitution method:<BR>\n" );
document.write( "3x+4y=6, 2x+8y=9<BR>\n" );
document.write( "5x+20y=3, 6x+7y=45 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515047 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=515047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Either there are typos, or whoever made up this problem meant to torture students with calculations.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Substitution is not the best method to solve systems like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x%2B4y=6%2C+2x%2B8y=9%29 ALIGN=MIDDLE  ALT=\"system%283x%2B4y=6%2C+2x%2B8y=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%285x%2B20y=3%2C+6x%2B7y=45%29 ALIGN=MIDDLE  ALT=\"system%285x%2B20y=3%2C+6x%2B7y=45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Substitution works best when one of the coefficients is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You look for a coefficient that is \"friendly\" and solve for that variable.<BR>\n" );
document.write( "When none of the coefficients is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > substitution makes you work with cumbersome fractions.<BR>\n" );
document.write( " <BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x%2B4y=6%2C+2x%2B8y=9%29 ALIGN=MIDDLE  ALT=\"system%283x%2B4y=6%2C+2x%2B8y=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > I would solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B8y=9 ALIGN=MIDDLE  ALT=\"2x%2B8y=9\"   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;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B8y=9 ALIGN=MIDDLE  ALT=\"2x%2B8y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-8y%2B9 ALIGN=MIDDLE  ALT=\"2x=-8y%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8y%2F2%2B9%2F2 ALIGN=MIDDLE  ALT=\"x=-8y%2F2%2B9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4y%2B9%2F2 ALIGN=MIDDLE  ALT=\"x=-4y%2B9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and then I would substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y%2B9%2F2 ALIGN=MIDDLE  ALT=\"-4y%2B9%2F2\"   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 the other equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x%2B4y=6%2C+x=-4y%2B9%2F2%29 ALIGN=MIDDLE  ALT=\"system%283x%2B4y=6%2C+x=-4y%2B9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28-4y%2B9%2F2%29%2B4y=6 ALIGN=MIDDLE  ALT=\"3%2A%28-4y%2B9%2F2%29%2B4y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12y%2B27%2F2%2B4y=6 ALIGN=MIDDLE  ALT=\"-12y%2B27%2F2%2B4y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8y%2B27%2F2=6 ALIGN=MIDDLE  ALT=\"-8y%2B27%2F2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2F2-6=8y ALIGN=MIDDLE  ALT=\"27%2F2-6=8y\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2F2-12%2F2=8y ALIGN=MIDDLE  ALT=\"27%2F2-12%2F2=8y\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F2=8y ALIGN=MIDDLE  ALT=\"15%2F2=8y\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15%2F2%2F8 ALIGN=MIDDLE  ALT=\"y=15%2F2%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=15%2F16%29 ALIGN=MIDDLE  ALT=\"highlight%28y=15%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=15%2F16%2C+x=-4y%2B9%2F2%29 ALIGN=MIDDLE  ALT=\"system%28y=15%2F16%2C+x=-4y%2B9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%2A%2815%2F16%29%2B9%2F2 ALIGN=MIDDLE  ALT=\"x=-4%2A%2815%2F16%29%2B9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-15%2F4%2B9%2F2 ALIGN=MIDDLE  ALT=\"x=-15%2F4%2B9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-15%2F4%2B18%2F4 ALIGN=MIDDLE  ALT=\"x=-15%2F4%2B18%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=3%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%285x%2B20y=3%2C+6x%2B7y=45%29 ALIGN=MIDDLE  ALT=\"system%285x%2B20y=3%2C+6x%2B7y=45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > I would solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B20y=3 ALIGN=MIDDLE  ALT=\"5x%2B20y=3\"   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;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B20y=3 ALIGN=MIDDLE  ALT=\"5x%2B20y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=-20y%2B3 ALIGN=MIDDLE  ALT=\"5x=-20y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-20y%2F5%2B3%2F5 ALIGN=MIDDLE  ALT=\"x=-20y%2F5%2B3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4y%2B3%2F5 ALIGN=MIDDLE  ALT=\"x=-4y%2B3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and then I would substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y%2B3%2F5 ALIGN=MIDDLE  ALT=\"-4y%2B3%2F5\"   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 the other equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=-4y%2B3%2F5%2C+6x%2B7y=45%29 ALIGN=MIDDLE  ALT=\"system%28x=-4y%2B3%2F5%2C+6x%2B7y=45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A%28-4y%2B3%2F5%29%2B7y=45 ALIGN=MIDDLE  ALT=\"6%2A%28-4y%2B3%2F5%29%2B7y=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24y%2B18%2F5%2B7y=45 ALIGN=MIDDLE  ALT=\"-24y%2B18%2F5%2B7y=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-17y%2B18%2F5=45 ALIGN=MIDDLE  ALT=\"-17y%2B18%2F5=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-17y=45-18%2F5 ALIGN=MIDDLE  ALT=\"-17y=45-18%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-17y=225%2F5-18%2F5 ALIGN=MIDDLE  ALT=\"-17y=225%2F5-18%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-17y=207%2F5 ALIGN=MIDDLE  ALT=\"-17y=207%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=207%2F5%2F%28-17%29 ALIGN=MIDDLE  ALT=\"y=207%2F5%2F%28-17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-207%2F85%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-207%2F85%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=-4y%2B3%2F5%2C+y=-207%2F85%29 ALIGN=MIDDLE  ALT=\"system%28x=-4y%2B3%2F5%2C+y=-207%2F85%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%2A%28-207%2F85%29%2B3%2F5 ALIGN=MIDDLE  ALT=\"x=-4%2A%28-207%2F85%29%2B3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=828%2F85%2B51%2F85 ALIGN=MIDDLE  ALT=\"x=828%2F85%2B51%2F85\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=879%2F85%29 ALIGN=MIDDLE  ALT=\"highlight%28x=879%2F85%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );