document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463148>Question 463148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which pair of equations does NOT have a common solution?<BR>\n" );
document.write( "a) x+y = -1; 4x-3y=24<BR>\n" );
document.write( "b)4x+6y=12; 6x+9y=12<BR>\n" );
document.write( "c) 2x-3y=-4; 2x+y=4<BR>\n" );
document.write( "d) 5x-4y=9; x-2y=-3\r<BR>\n" );
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document.write( "Please Explain solution\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317375 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=317375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Which pair of equations does NOT have a common solution?<BR>\n" );
document.write( "a) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By+=+-1 ALIGN=MIDDLE  ALT=\"x%2By+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-3y=24 ALIGN=MIDDLE  ALT=\"4x-3y=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B6y=12 ALIGN=MIDDLE  ALT=\"4x%2B6y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B9y=12 ALIGN=MIDDLE  ALT=\"6x%2B9y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=-4 ALIGN=MIDDLE  ALT=\"2x-3y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By=4 ALIGN=MIDDLE  ALT=\"2x%2By=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-4y=9 ALIGN=MIDDLE  ALT=\"5x-4y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=-3 ALIGN=MIDDLE  ALT=\"x-2y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "easiest way is to write all of them in slope-intercept form and see if any of them are parallel lines; parallel lines do NOT have a common solution\r<BR>\n" );
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document.write( "a) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=-x-1 ALIGN=MIDDLE  ALT=\"y+=-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >...slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   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=4x-24=3y ALIGN=MIDDLE  ALT=\"4x-24=3y\"   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=%284%2F3%29x-8=y ALIGN=MIDDLE  ALT=\"%284%2F3%29x-8=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >..slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29 ALIGN=MIDDLE  ALT=\"%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B6y=12 ALIGN=MIDDLE  ALT=\"4x%2B6y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y=-4x%2B12 ALIGN=MIDDLE  ALT=\"6y=-4x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F6%29x%2B2 ALIGN=MIDDLE  ALT=\"y=-%284%2F6%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%282%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y=-%282%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282%2F3%29 ALIGN=MIDDLE  ALT=\"-%282%2F3%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=6x%2B9y=12 ALIGN=MIDDLE  ALT=\"6x%2B9y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9y=-6x%2B12 ALIGN=MIDDLE  ALT=\"9y=-6x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%286%2F9%29x%2B12%2F9 ALIGN=MIDDLE  ALT=\"y=-%286%2F9%29x%2B12%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%282%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=-%282%2F3%29x%2B4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >...slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282%2F3%29 ALIGN=MIDDLE  ALT=\"-%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=-4 ALIGN=MIDDLE  ALT=\"2x-3y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B4=3y ALIGN=MIDDLE  ALT=\"2x%2B4=3y\"   DISABLED_style= \"max-width:90%; height:auto;\" > .....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x%2B4%2F3=y ALIGN=MIDDLE  ALT=\"%282%2F3%29x%2B4%2F3=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29 ALIGN=MIDDLE  ALT=\"%282%2F3%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=2x%2By=4 ALIGN=MIDDLE  ALT=\"2x%2By=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B4 ALIGN=MIDDLE  ALT=\"y=-2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >...slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-4y=9 ALIGN=MIDDLE  ALT=\"5x-4y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-9=4y ALIGN=MIDDLE  ALT=\"5x-9=4y\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F4%29x-9%2F4=y ALIGN=MIDDLE  ALT=\"%285%2F4%29x-9%2F4=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >..slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F4%29 ALIGN=MIDDLE  ALT=\"%285%2F4%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=x-2y=-3 ALIGN=MIDDLE  ALT=\"x-2y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3=2y ALIGN=MIDDLE  ALT=\"x%2B3=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x%2B3%2F2=y ALIGN=MIDDLE  ALT=\"%281%2F2%29x%2B3%2F2=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as you can see, only \r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B6y=12 ALIGN=MIDDLE  ALT=\"4x%2B6y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B9y=12 ALIGN=MIDDLE  ALT=\"6x%2B9y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > have same slope..\r<BR>\n" );
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document.write( "let's see if these lines are parallel:\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+-10%2C+10%2C+-10%2C+10%2C+-%282%2F3%29x%2B2%2C-%282%2F3%29x%2B4%2F3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, your answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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