Question

For what value of k will the following pair of linear equations have no solution?

2x + 3y = 9, 6x + (k – 2)y = (3k – 2)

Answer 1

For no solution, we have `(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)`.

∴ `2/6 = 3/(k - 2)` and `2/6 ≠ 9/(3k - 2)`

⇒ `3/(k - 2) = 1/3` and `9/(3k - 2) ≠ 1/3`

⇒ k – 2 = 9 and 3k – 2 ≠ 27

⇒ k = 11 and `k ≠ 29/3`.

Hence, k = 11.