document.write( "Question 444233: When does the system
\n" ); document.write( "\"kx%2B3y=-6\"
\n" ); document.write( "\"x%2B%28k%2B2%29y=2\"
\n" ); document.write( "have a unique solution? \r
\n" ); document.write( "\n" ); document.write( "Thanks :) \n" ); document.write( "
Algebra.Com's Answer #306286 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
When does the system
\n" ); document.write( "kx+3y=-6
\n" ); document.write( "x+(k+2)y=2
\n" ); document.write( "have a unique solution?
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\n" ); document.write( "The slopes must be different.
\n" ); document.write( "y = (-6-kx)/3
\n" ); document.write( "slope = -k/3
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\n" ); document.write( "y = (-x+2)/(k+2)
\n" ); document.write( "slope = -1/(k+2)
\n" ); document.write( "--------------------
\n" ); document.write( "Solve:
\n" ); document.write( "-k/3 = -1/(k+2)
\n" ); document.write( "Cross-multiply:
\n" ); document.write( "-k^2-2k = -3
\n" ); document.write( "k^2+2k-3 = 0
\n" ); document.write( "(k+3)(k-1) = 0
\n" ); document.write( "k = -3 or k = 1
\n" ); document.write( "-----------------------
\n" ); document.write( "The system has a unique solution as long as
\n" ); document.write( "k does not = -3 or 1.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( " \n" ); document.write( "
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