Question

Find the value of k for which the system of equations 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, `a_1 = k, b_1 = -1, c_1 = -2, a_2 = 6, b_2 = -2 and c_2 = -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.