document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=362348>Question 362348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you know when an equation has infinetly many solutions, and when an equation has no solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #258204 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=258204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When your equations lead to an inconsistency, such as, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=0 ALIGN=MIDDLE  ALT=\"1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or similar, then you have two parallel lines with no solution.<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=12 ALIGN=MIDDLE  ALT=\"2x%2By=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=5 ALIGN=MIDDLE  ALT=\"2x%2By=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract eq. 2 from eq. 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By-2x-y=12-5 ALIGN=MIDDLE  ALT=\"2x%2By-2x-y=12-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=7 ALIGN=MIDDLE  ALT=\"0=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "No solution, the lines are parallel.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "When your equations lead to an identity, such as, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=5 ALIGN=MIDDLE  ALT=\"5=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or similar, then you have two lines that are the same line and have infinitely many solutions.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=6 ALIGN=MIDDLE  ALT=\"2x%2By=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B2y=12 ALIGN=MIDDLE  ALT=\"4x%2B2y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply eq. 1 by -2 and add to eq. 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-2y%2B4x%2B2y=-12%2B12 ALIGN=MIDDLE  ALT=\"-4x-2y%2B4x%2B2y=-12%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The lines are the same line (eq. 2 is 2 times eq. 1), there are infinitely many solutions (every solution of eq. 1 is also a solution of eq. 2).<BR>\n" );
document.write( " </SPAN>\n" );
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