document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=226054>Question 226054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem.\r<BR>\n" );
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document.write( "Use substitution to solve each system of equation? State whether it has no solution or many solutions.\r<BR>\n" );
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document.write( "x+5y=-3<BR>\n" );
document.write( "3x-2y=8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #168449 by </B><A HREF=/tutors/aboutme.mpl?userid=LtAurora><B>LtAurora(115)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LtAurora><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=LtAurora><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=168449\">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=x%2B5y=-3 ALIGN=MIDDLE  ALT=\"x%2B5y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y=8 ALIGN=MIDDLE  ALT=\"3x-2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first equation is easiest to get a variable by itself, so move the 5y to the other side bu subtracting it from both:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3-5y ALIGN=MIDDLE  ALT=\"x=-3-5y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then we can plug this into the second equation for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28-3-5y%29-2y=8 ALIGN=MIDDLE  ALT=\"3%28-3-5y%29-2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distribute the 3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9-15y-2y=8 ALIGN=MIDDLE  ALT=\"-9-15y-2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9-17y=8 ALIGN=MIDDLE  ALT=\"-9-17y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Move the -9 to the other side by adding it:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-17y=17 ALIGN=MIDDLE  ALT=\"-17y=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by -17:<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( "We can plug this back in to get x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3-5%28-1%29 ALIGN=MIDDLE  ALT=\"x=-3-5%28-1%29\"   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%2B5 ALIGN=MIDDLE  ALT=\"x=-3%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the answer is (2,-1). It has only one solution as the lines cross at that point. </SPAN>\n" );
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