document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=621375>Question 621375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3x - 8y = 2<BR>\n" );
document.write( "4x - 4y = 32 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390800 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=390800\">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=system%283x+-+8y+=+2%2C4x+-+4y+=+32%29 ALIGN=MIDDLE  ALT=\"system%283x+-+8y+=+2%2C4x+-+4y+=+32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A combination equation (made by multiplying equations times factors as needed and adding them) can replace one of the equations in a system to make an equivalent system.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x+-+8y+=+2%2C4x+-+4y+=+32%29 ALIGN=MIDDLE  ALT=\"system%283x+-+8y+=+2%2C4x+-+4y+=+32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22times+%28-1%29%22%2C+%22times%282%29%22%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22times+%28-1%29%22%2C+%22times%282%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28125%2C80%2C0%2C5%2C0%2C3.2%2C%0D%0Alocate%280.3%2C2.8%2C-3x+%2B+8y+=+-2%29%2Clocate%280.8%2C2%2C8x+-+8y+=+64%29%2C%0D%0Aline%280.2%2C1.1%2C4.8%2C1.1%29%2Clocate%281.2%2C1%2C5x=64-2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=62 ALIGN=MIDDLE  ALT=\"5x=62\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2F5=62%2F5 ALIGN=MIDDLE  ALT=\"5x%2F5=62%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=62%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28x=62%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=62%2F5%2C4x+-+4y+=+32%29 ALIGN=MIDDLE  ALT=\"system%28x=62%2F5%2C4x+-+4y+=+32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C1%2C%22times+1%22%2C+times+%28-1%2F4%29%29 ALIGN=MIDDLE  ALT=\"matrix%282%2C1%2C%22times+1%22%2C+times+%28-1%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28125%2C125%2C0%2C5%2C-0.5%2C4%2C%0D%0Alocate%280.8%2C3.5%2Cx%29%2Clocate%282%2C3.5%2C%22=%22%29%2C%0D%0Alocate%282.5%2C3.5%2C62%2F5%29%2Clocate%280.2%2C2%2C-x%2By=-8%29%2C%0D%0Aline%280.2%2C1.1%2C4.8%2C1.1%29%2Clocate%281.5%2C1%2Cy=62%2F5-8%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=62%2F5-40%2F5 ALIGN=MIDDLE  ALT=\"y=62%2F5-40%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=22%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28y=22%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "SOLVING BY SUBSTITUTION<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-4y=32 ALIGN=MIDDLE  ALT=\"4x-4y=32\"   DISABLED_style= \"max-width:90%; height:auto;\" > --(dividing both sides by 4)--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=8 ALIGN=MIDDLE  ALT=\"x-y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y%2By=8%2By ALIGN=MIDDLE  ALT=\"x-y%2By=8%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%2B8 ALIGN=MIDDLE  ALT=\"x=y%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-8y=2 ALIGN=MIDDLE  ALT=\"3x-8y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --(multiplying both sides by (-1)) --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B8y=-2 ALIGN=MIDDLE  ALT=\"-3x%2B8y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and substituting the expression for x found before<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B8y=-2 ALIGN=MIDDLE  ALT=\"-3x%2B8y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%28y%2B8%29-8y=-2 ALIGN=MIDDLE  ALT=\"-3%28y%2B8%29-8y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y-24%2B8y=-2 ALIGN=MIDDLE  ALT=\"-3y-24%2B8y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24%2B5y=-2 ALIGN=MIDDLE  ALT=\"-24%2B5y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24%2B5y%2B24=-2%2B24 ALIGN=MIDDLE  ALT=\"-24%2B5y%2B24=-2%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=22 ALIGN=MIDDLE  ALT=\"5y=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y%2F5=2%2F52 ALIGN=MIDDLE  ALT=\"5y%2F5=2%2F52\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=22%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28y=22%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and that value can be substituted in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%2B8 ALIGN=MIDDLE  ALT=\"x=y%2B8\"   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=x=22%2F5%2B8 ALIGN=MIDDLE  ALT=\"x=22%2F5%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=22%2F5%2B40%2F5 ALIGN=MIDDLE  ALT=\"x=22%2F5%2B40%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=62%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28x=62%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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