Question

For what value of k the following system of equation will be inconsistent kx + 3y = K - 3 and 12x + ky = k

Answer 1

For inconsistent, a1/a2=b1/b2not equal to c1/c2

Comparing equation 1 with a1x+b1y=c1

And equation 2 with a2x+b2y=c2

a1/a2=k/12
b1/b2=3/k
c1/c2=k-3/k

Now a1/a2=b1/b2
k/12=3/k
k^2=36k=+-6

If k = +6
b1/b2is not equal to c1/c2
b1/b2=3/6=1/2
c1/c2=6-3/6=3/6
so c1/c2=b1/b2 But this contradicts that b1/b2 is not equal to c1/c2

So k= -6

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