document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152569>Question 152569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many solutions are in the equation: (-2x+y=1, -4x+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 #112144 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=112144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Start with the given system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-2x%2By=1%2C-4x%2B2y=-8%29 ALIGN=MIDDLE  ALT=\"system%28-2x%2By=1%2C-4x%2B2y=-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=-2%28-2x%2By%29=-2%281%29 ALIGN=MIDDLE  ALT=\"-2%28-2x%2By%29=-2%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by -2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-2y=-2 ALIGN=MIDDLE  ALT=\"4x-2y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So we have the new system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%284x-2y=-2%2C-4x%2B2y=-8%29 ALIGN=MIDDLE  ALT=\"system%284x-2y=-2%2C-4x%2B2y=-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x-2y%29%2B%28-4x%2B2y%29=%28-2%29%2B%28-8%29 ALIGN=MIDDLE  ALT=\"%284x-2y%29%2B%28-4x%2B2y%29=%28-2%29%2B%28-8%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=%284x%2B-4x%29%2B%28-2y%2B2y%29=-2%2B-8 ALIGN=MIDDLE  ALT=\"%284x%2B-4x%29%2B%28-2y%2B2y%29=-2%2B-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B0y=-10 ALIGN=MIDDLE  ALT=\"0x%2B0y=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. Notice how the x terms cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-10 ALIGN=MIDDLE  ALT=\"0=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >Simplify.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-10 ALIGN=MIDDLE  ALT=\"0=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <font size=\"4\"><b>never</b></font> true, this means that there are no solutions. So the system is inconsistent.<BR>\n" );
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