document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=734890>Question 734890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I can't get the answer to the following problem ; \r<BR>\n" );
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document.write( "y-5x=-2<BR>\n" );
document.write( "3x-7y=22\r<BR>\n" );
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document.write( "The instructions say to use the substitution method.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #449174 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=449174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Substitution means that your first step is solving for one variable in one of the equations. For example<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5x=-2 ALIGN=MIDDLE  ALT=\"y-5x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-2 ALIGN=MIDDLE  ALT=\"y=5x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note: Look for a variable that has no visible coefficient. In this case, the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5x=-2 ALIGN=MIDDLE  ALT=\"y-5x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an invisible number 1.<BR>\n" );
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document.write( "The second step when using substitution is to substitute the expression found for the variable in the other equation.<BR>\n" );
document.write( "In this case, since we found that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-2 ALIGN=MIDDLE  ALT=\"y=5x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we write (5x-2) instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-7y=22 ALIGN=MIDDLE  ALT=\"3x-7y=22\"   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=3x-7%285x-2%29=22 ALIGN=MIDDLE  ALT=\"3x-7%285x-2%29=22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "No we use the distributive property to transform that into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-7%2A%285x%29-7%2A%28-2%29=22 ALIGN=MIDDLE  ALT=\"3x-7%2A%285x%29-7%2A%28-2%29=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-35x%2B14=22 ALIGN=MIDDLE  ALT=\"3x-35x%2B14=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32x%2B14=22 ALIGN=MIDDLE  ALT=\"-32x%2B14=22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then we solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32x%2B14=22 ALIGN=MIDDLE  ALT=\"-32x%2B14=22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32x%2B14=22 ALIGN=MIDDLE  ALT=\"-32x%2B14=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32x=22%7D-14%7D%7D+--%3E+%7B%7B%7B-32x=8 ALIGN=MIDDLE  ALT=\"-32x=22%7D-14%7D%7D+--%3E+%7B%7B%7B-32x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2F%28-32%29 ALIGN=MIDDLE  ALT=\"x=8%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-1%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "As a final step, we substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F4 ALIGN=MIDDLE  ALT=\"-1%2F4\"   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;\" > somewhere to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "It may be easiest to use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x-2 ALIGN=MIDDLE  ALT=\"y=5x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%28-1%2F4%29-2 ALIGN=MIDDLE  ALT=\"y=5%28-1%2F4%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%2F4-2 ALIGN=MIDDLE  ALT=\"y=-5%2F4-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%2F4-8%2F4 ALIGN=MIDDLE  ALT=\"y=-5%2F4-8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-13%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-13%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "NOTE: If you cannot find a variable with no visible coefficient, substitution will get cumbersome, as you would be working with fractions a lot. In that case, it is better to use a different method. </SPAN>\n" );
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