document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=427061>Question 427061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system of equations using substitution.\r<BR>\n" );
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document.write( "2x+4y=12<BR>\n" );
document.write( "4x+16y=8\r<BR>\n" );
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document.write( "I substituted 2x+4y for x in the second equation and I ended up with 8x+32y=8. I've tried so many of these problems and I just can't understand them. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297009 by </B><A HREF=/tutors/aboutme.mpl?userid=Gogonati><B>Gogonati(855)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Gogonati><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=Gogonati><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=297009\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solution:First we simplify the system dividing the first equation by 2 and the second by 4,and the system can be written:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2B2y=6%2C+x%2B4y=2%29 ALIGN=MIDDLE  ALT=\"system%28x%2B2y=6%2C+x%2B4y=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Express x in the first equation with respect to y and substitute in the second equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=6-2y%2C+6-2y%2B4y=2%29 ALIGN=MIDDLE  ALT=\"system%28x=6-2y%2C+6-2y%2B4y=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The second equation is a linear equation of one variable. We solve this equation with respect to y:\r<BR>\n" );
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document.write( "6+2y=2 => 2y=-4 => y=-2. Substitute this value of y in the first equation and find x: x=6-2(-2) => x=10. The ordered pair (10, -2) is the solution of our system.\r<BR>\n" );
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document.write( "Check: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%282%2A10%2B4%2A%28-2%29=12%2C+4%2A10%2B16%2A%28-2%29=8%29 ALIGN=MIDDLE  ALT=\"+system%282%2A10%2B4%2A%28-2%29=12%2C+4%2A10%2B16%2A%28-2%29=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "       <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%2820-8=12%2C+40-32=8%29 ALIGN=MIDDLE  ALT=\"+system%2820-8=12%2C+40-32=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "        <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2812=12%2C+8=8%29 ALIGN=MIDDLE  ALT=\"system%2812=12%2C+8=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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