document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=649252>Question 649252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the value of k for which the system of linear equations<BR>\n" );
document.write( "2x&#8722;y =5<BR>\n" );
document.write( "6x+ky=2<BR>\n" );
document.write( "Has no solution.<BR>\n" );
document.write( "k=? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406907 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=406907\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Now we want a system with no solutions. This mean the slopes are the same, <BR>\n" );
document.write( "but the y-intercepts are different,the lines are parallel . Again, let's get these into slop-intercept form. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y+=5 ALIGN=MIDDLE  ALT=\"2x-y+=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >....->...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-5 ALIGN=MIDDLE  ALT=\"y=2x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2Bky=2 ALIGN=MIDDLE  ALT=\"6x%2Bky=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...->....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%286%2Fk%29x%2B2%2Fk ALIGN=MIDDLE  ALT=\"y=-%286%2Fk%29x%2B2%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Again, we set the slopes equal to each other. This gives us 2 = -(6/k). <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k+=+-6 ALIGN=MIDDLE  ALT=\"2k+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-6%2F2 ALIGN=MIDDLE  ALT=\"k+=+-6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=-3%29 ALIGN=MIDDLE  ALT=\"highlight%28k=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we need to verify that the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-intercepts ALIGN=MIDDLE  ALT=\"y-intercepts\"   DISABLED_style= \"max-width:90%; height:auto;\" > are not the same. <BR>\n" );
document.write( " first substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%286%2Fk%29x%2B2%2Fk ALIGN=MIDDLE  ALT=\"y=-%286%2Fk%29x%2B2%2Fk\"   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=y=-%286%2F-3%29x%2B2%2F-3 ALIGN=MIDDLE  ALT=\"y=-%286%2F-3%29x%2B2%2F-3\"   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=y=2x-2%2F3 ALIGN=MIDDLE  ALT=\"y=2x-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " The first one is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the second one is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fk ALIGN=MIDDLE  ALT=\"2%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "They clearly are not the same, so the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system+ ALIGN=MIDDLE  ALT=\"system+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=has ALIGN=MIDDLE  ALT=\"has\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C0%2C2x-5%2C2x-2%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C0%2C2x-5%2C2x-2%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );