document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=658850>Question 658850</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the values of k such that the system of linear equations does not have a unique solution. (Enter your answers as a comma-separated list.)<BR>\n" );
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document.write( "x\r<BR>\n" );
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document.write( "y\r<BR>\n" );
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document.write( "kz\r<BR>\n" );
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document.write( " = \r<BR>\n" );
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document.write( "9\r<BR>\n" );
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document.write( "x\r<BR>\n" );
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document.write( "ky\r<BR>\n" );
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document.write( "z\r<BR>\n" );
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document.write( " = \r<BR>\n" );
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document.write( "6\r<BR>\n" );
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document.write( "kx\r<BR>\n" );
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document.write( "y\r<BR>\n" );
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document.write( "z\r<BR>\n" );
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document.write( " = \r<BR>\n" );
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document.write( "5<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410499 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=410499\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Add all three equations together. You'll get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bkz=9 ALIGN=MIDDLE  ALT=\"x%2By%2Bkz=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bky%2Bz=6 ALIGN=MIDDLE  ALT=\"x%2Bky%2Bz=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >............2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kx%2By%2Bz=5 ALIGN=MIDDLE  ALT=\"kx%2By%2Bz=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.................3<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bx%2Bkx%2By%2Bky%2By%2Bkz%2Bz%2Bz=9%2B6%2B5 ALIGN=MIDDLE  ALT=\"x%2Bx%2Bkx%2By%2Bky%2By%2Bkz%2Bz%2Bz=9%2B6%2B5\"   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%2B2y%2B2z%2Bkx%2Bky%2Bkz=20 ALIGN=MIDDLE  ALT=\"2x%2B2y%2B2z%2Bkx%2Bky%2Bkz=20\"   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%28x%2By%2Bz%29%2Bk%28x%2By%2Bz%29=20 ALIGN=MIDDLE  ALT=\"2%28x%2By%2Bz%29%2Bk%28x%2By%2Bz%29=20\"   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=%282%2Bk%29%28x%2By%2Bz%29=20 ALIGN=MIDDLE  ALT=\"%282%2Bk%29%28x%2By%2Bz%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >....when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Bk%29=0 ALIGN=MIDDLE  ALT=\"%282%2Bk%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Bk%29%28x%2By%2Bz%29=0 ALIGN=MIDDLE  ALT=\"%282%2Bk%29%28x%2By%2Bz%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and that will be if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-2 ALIGN=MIDDLE  ALT=\"k=-2\"   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=0%28x%2By%2Bz%29=20 ALIGN=MIDDLE  ALT=\"0%28x%2By%2Bz%29=20\"   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=0%2Ax%2B0%2Ay%2B0%2Az=20+ ALIGN=MIDDLE  ALT=\"0%2Ax%2B0%2Ay%2B0%2Az=20+\"   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=0=20 ALIGN=MIDDLE  ALT=\"0=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=impossible ALIGN=MIDDLE  ALT=\"impossible\"   DISABLED_style= \"max-width:90%; height:auto;\" >, meaning there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=solutions ALIGN=MIDDLE  ALT=\"solutions\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=unique ALIGN=MIDDLE  ALT=\"unique\"   DISABLED_style= \"max-width:90%; height:auto;\" > solutions if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28k=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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