document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103928>Question 103928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you're solving a system of 2 linear equations and you come up with the equation 0 = -5. What does that tell you about the relationship of the two lines? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75609 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=75609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say you have the two equations: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B1 ALIGN=MIDDLE  ALT=\"y=2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-4 ALIGN=MIDDLE  ALT=\"y=2x-4\"   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=2x%2B1=2x-4 ALIGN=MIDDLE  ALT=\"2x%2B1=2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the two equations equal to one another\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1-2x=-4 ALIGN=MIDDLE  ALT=\"2x%2B1-2x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2x=-4-1 ALIGN=MIDDLE  ALT=\"2x-2x=-4-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x=-5 ALIGN=MIDDLE  ALT=\"0x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-5 ALIGN=MIDDLE  ALT=\"0=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Notice we have a contradiction (0 will never be equal to -5). Since this statement is never true, there are no solutions.\r<BR>\n" );
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document.write( "Notice if we graph the two equations, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-6%2C+5%2C+-10%2C+10%2C2x%2B1%2C2x-4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-6%2C+5%2C+-10%2C+10%2C2x%2B1%2C2x-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B1 ALIGN=MIDDLE  ALT=\"y=2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-4 ALIGN=MIDDLE  ALT=\"y=2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green)\r<BR>\n" );
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document.write( "Notice the two lines are parallel and will never intersect. So this means the system has no solutions. </SPAN>\n" );
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