The number of values of k, for which the system of equations (k+1)x + 8y = 4k; kx + (k+3)y = 3k has no solution, is:

For no solution
(k+1)/k = 8/(k+3) ≠ 4k/3k
(1) ⇒ (k+1)(k+3) = 8k or k² + 4k + 3 = 8k
k² - 4k + 3 = 0
(k-1)(k-3) = 0
k = 1, 3
But for k = 1, equation (1) is not satisfied
Hence k = 3.