document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176262>Question 176262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me how to use the substitution method to solve this system of equations.\r<BR>\n" );
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document.write( "3x-11y=2<BR>\n" );
document.write( "x-5y=2\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131381 by </B><A HREF=/tutors/aboutme.mpl?userid=EMStelley><B>EMStelley(208)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=EMStelley><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=EMStelley><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=131381\">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=3x-11y=2 ALIGN=MIDDLE  ALT=\"3x-11y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5y=2 ALIGN=MIDDLE  ALT=\"x-5y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The substitution method involves using one equation to solve for one of the variables, and then substituting back in to the other equation.  For example, in the second equation we can easily solve for x by adding 5y to both sides, obtaining<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5y%2B2 ALIGN=MIDDLE  ALT=\"x=5y%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, we replace the x in the first equation with 5y+2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%285y%2B2%29-11y=2 ALIGN=MIDDLE  ALT=\"3%285y%2B2%29-11y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15y%2B6-11y=2 ALIGN=MIDDLE  ALT=\"15y%2B6-11y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=-4 ALIGN=MIDDLE  ALT=\"4y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find x, we plug in y=-1 into either equation.  I will use the second one for simplicity:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5%28-1%29=2 ALIGN=MIDDLE  ALT=\"x-5%28-1%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=2 ALIGN=MIDDLE  ALT=\"x%2B5=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the solution is (-3,-1). </SPAN>\n" );
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