For what value of k, the following pair of line is equations have infinite number of solutions: kx+3y=(2k+1); 2(k+1)x +9y=(7k+1).
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kx+3y=2k+1---------(I)
2(k+1)x+9y=7k+1
=>2kx+2x+9y=7k+1-----(ii)
Equation (I) *2=2kx+6y=4k+2
(ii) *1=2kx+2x+9y=7k+1
(-) (-) (-) (-) (-)
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-2x-3y= -3k+1
=>3k=-2x-3y/-1
=>k=2x+3y/3
2(k+1)x+9y=7k+1
=>2kx+2x+9y=7k+1-----(ii)
Equation (I) *2=2kx+6y=4k+2
(ii) *1=2kx+2x+9y=7k+1
(-) (-) (-) (-) (-)
---------------------------------
-2x-3y= -3k+1
=>3k=-2x-3y/-1
=>k=2x+3y/3
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