For what integral value of k, the system of equations kx - 5y + 6 = 0 and 4(k - 1)y - 12x + 3 = 0 has no solution ?

Explanation

For a system to have no solution, \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}. Solving \frac{k}{-12} = \frac{-5}{4(k-1)} leads to k^2 - k - 15 = 0, which yields irrational roots. Hence, no integral value for k exists.

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