Question

The number of values of k for which the system of equations (k + 1)x + 8y = 4k, kx + (k + 3)y = 3k - 1 has infinitely many solutions is 

(A) 0 

(B) 1 

(C) 2 

(D) infinite  

Answer 1

Answer is (B) 1

Here Δ = 0 for k = 3, 1; Δ_x = 0 for k = 2, 1, Δ_y = 0 for k = 1. 

Hence, k = 1.

Alternate method:

For infinitely many solutions the two equations become identical, so

(k + 1)/k = 8/(k + 3) = 4k/(3k - 1) ⇒ k = 1