document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1147938>Question 1147938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following system of equations, what positive value of k would make the lines below parallel? kx+2y=8  and 18x+ky=12\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 #769277 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=769277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kx%2B2y=8 ALIGN=MIDDLE  ALT=\"kx%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%2Bky=12 ALIGN=MIDDLE  ALT=\"18x%2Bky=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find: what positive value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > would make the lines below parallel?\r<BR>\n" );
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document.write( "recall that  parallel line have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope ALIGN=MIDDLE  ALT=\"slope\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, write both equations in slope intercept form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kx%2B2y=8 ALIGN=MIDDLE  ALT=\"kx%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=2y=-kx%2B8 ALIGN=MIDDLE  ALT=\"2y=-kx%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...both sides divide by <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%28k%2F2%29x%2B4 ALIGN=MIDDLE  ALT=\"y=-%28k%2F2%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > => slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28k%2F2%29 ALIGN=MIDDLE  ALT=\"-%28k%2F2%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=18x%2Bky=12 ALIGN=MIDDLE  ALT=\"18x%2Bky=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....take same steps as above\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ky=-18x%2B12 ALIGN=MIDDLE  ALT=\"ky=-18x%2B12\"   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=-%2818%2Fk%29x%2B12%2Fk ALIGN=MIDDLE  ALT=\"y=-%2818%2Fk%29x%2B12%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" > => slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2818%2Fk%29 ALIGN=MIDDLE  ALT=\"-%2818%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slopes ALIGN=MIDDLE  ALT=\"slopes\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28k%2F2%29=-%2818%2Fk%29 ALIGN=MIDDLE  ALT=\"-%28k%2F2%29=-%2818%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, first cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28k%29k=-%2818%292 ALIGN=MIDDLE  ALT=\"-%28k%29k=-%2818%292\"   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=-k%5E2=-36 ALIGN=MIDDLE  ALT=\"-k%5E2=-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >......both sides multiply by <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=k%5E2=36 ALIGN=MIDDLE  ALT=\"k%5E2=36\"   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=k=sqrt%2836%29 ALIGN=MIDDLE  ALT=\"k=sqrt%2836%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=highlight%28k=6%29 ALIGN=MIDDLE  ALT=\"highlight%28k=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>positive value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > that we need\r<BR>\n" );
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document.write( "and, your lines are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B2y=8 ALIGN=MIDDLE  ALT=\"6x%2B2y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%2B6y=12 ALIGN=MIDDLE  ALT=\"18x%2B6y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or in slope intercept form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%286%2F2%29x%2B4 ALIGN=MIDDLE  ALT=\"y=-%286%2F2%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2B4 ALIGN=MIDDLE  ALT=\"y=-3x%2B4\"   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=-%2818%2F6%29x%2B12%2F6 ALIGN=MIDDLE  ALT=\"y=-%2818%2F6%29x%2B12%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2B2 ALIGN=MIDDLE  ALT=\"y=-3x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "proof with a graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B4%2C+-3x%2B2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B4%2C+-3x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as you can see, the lines are parallel if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=6%29 ALIGN=MIDDLE  ALT=\"highlight%28k=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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