Question

Find the value of k for which the system of equations kx – y = 2 and 6x – 2y = 3 has a unique solution.

Find k for which the system kx – y = 2 and 6x – 2y = 3 has a unique solution.

Answer 1

The given system is

kx – y – 2 = 0   ...(i)

6x – 2y – 3 = 0   ...(ii)

Here, a₁ = k, b₁ = –1, c₁ = –2, a₂ = 6, b₂ = –2 and c₂ = –3

For the system, to have a unique solution, we must have

`(a_1)/(a_2) ≠ (b_1)/(b_2)`

⇒ `k/6 ≠ (-1)/(-2) = 1/2`

⇒ k ≠ 3

Hence, k ≠ 3.