Question

The value of k for which the system of equations x + y – 4 = 0 and 2x + ky = 3, has no solution, is ______.

Options

• – 2

• ≠ 2

• 3

• 2

Answer 1

The value of k for which the system of equations x + y – 4 = 0 and 2x + ky = 3, has no solution, is 2.

Explanation:

Given equations:

x + y – 4 = 0 and 2x + ky – 3 = 0

Here, `a_1/a_2 = 1/2, b_1/b_2 = 1/k` and `c_1/c_2 = (-4)/(-3) = 4/3`

∵ System has no solution

∴ `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

⇒ `1/2 = 1/k ≠ 4/3`

⇒ k = 2 or `k ≠ 3/4`