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Question

For what value of ‘K’ will the following pair of linear equations have infinitely many solutions
Kx+3y=k-3; 12x+ky=k
[or kx+3y-k+3=0 ; 12x+ky-k=0]

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Solution

kx+3y=k-3
12x+ky=k
compare with a1x+b1y=c1
a2x+b2y=c2
a1=k,a2=12,b1=3,b2=k
c1=k3,c2=k
For infinite solutions, a1a2=b1b2=c1c2
k12=3k=k3k
k12=3kk2=36
k=6.

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