document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=372417>Question 372417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem says solve by substitution <BR>\n" );
document.write( "to find the solution of<BR>\n" );
document.write( "5x+5y=-20<BR>\n" );
document.write( "and -9x+y=76<BR>\n" );
document.write( "there may not be a solution as well but that is where I get confused. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #265262 by </B><A HREF=/tutors/aboutme.mpl?userid=marcsam823><B>marcsam823(57)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=marcsam823><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=265262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5x +5y = -20 <BR>\n" );
document.write( "-9x + y = 76\r<BR>\n" );
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document.write( "To solve by substitution solve one equation for one variable and substitute that value into the second.  There are several ways to do this with problems of this type.\r<BR>\n" );
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document.write( "Let's start with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+5y+=+-20 ALIGN=MIDDLE  ALT=\"5x+%2B+5y+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide each term by 5:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2F5+%2B+5y%2F5+=-20%2F5 ALIGN=MIDDLE  ALT=\"5x%2F5+%2B+5y%2F5+=-20%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+-4 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can now easily solve for x or y.  Let's solve for y by subtracting x from both sides of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x+-4 ALIGN=MIDDLE  ALT=\"y+=+-x+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In the second equation, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x-4 ALIGN=MIDDLE  ALT=\"-x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > for y \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x+%2B+y+=76 ALIGN=MIDDLE  ALT=\"-9x+%2B+y+=76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x+%2B+%28-x+-4%29+=76 ALIGN=MIDDLE  ALT=\"-9x+%2B+%28-x+-4%29+=76\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have only one variable (x) and can solve for it.\r<BR>\n" );
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document.write( "Combine like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10x+-+4+=+76 ALIGN=MIDDLE  ALT=\"-10x+-+4+=+76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 4 to both sides of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10x+=+80 ALIGN=MIDDLE  ALT=\"-10x+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve for x by dividing both sides by -10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-8 ALIGN=MIDDLE  ALT=\"x+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To solve for y,  plug x = -8 into either one of the original equations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+5y+=+-20 ALIGN=MIDDLE  ALT=\"5x+%2B+5y+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28-8%29+%2B+5y+=+-20 ALIGN=MIDDLE  ALT=\"5%28-8%29+%2B+5y+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-40+%2B+5y+=+-20 ALIGN=MIDDLE  ALT=\"-40+%2B+5y+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=+20 ALIGN=MIDDLE  ALT=\"5y+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4 ALIGN=MIDDLE  ALT=\"y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To further verify that x = -8 and y = 4, check by substituting these values into the other equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x+%2B+y+=+76 ALIGN=MIDDLE  ALT=\"-9x+%2B+y+=+76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%28-8%29+%2B+4+=+76 ALIGN=MIDDLE  ALT=\"-9%28-8%29+%2B+4+=+76\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72+%2B+4+=+76 ALIGN=MIDDLE  ALT=\"72+%2B+4+=+76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76+=+76 ALIGN=MIDDLE  ALT=\"76+=+76\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The correct answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-8 ALIGN=MIDDLE  ALT=\"x+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4 ALIGN=MIDDLE  ALT=\"y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There will be instances where there is no solution.  If you solve for x and y in the first equation and the results do not fit into the second, then there is no solution.  Be aware that your textbook may present you with a problem like that.  </SPAN>\n" );
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