Question

X-ky=12; 3x+2y=-5 find k if there exists a unique solution

Answer 1

x - ky = 2 ; 3x + 2y = -5

a1 = 1, b1 = -k ; a2 = 3, b2 = 2

For a unique solution,

a1/a2 ≠ b1/b2

1/3 ≠ -k/2

2/3 ≠ -k

k ≠ -2/3

Therefore, for any value of k except -2/3, the given system has a unique solution.