Question

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

Answer 1

Given: x + y – 4 = 0 and 2x + ky – 3 = 0

Let a₁ = 1, b₁ = 1, c₁ = –4 and a₂ = 2, b₂ = k, c₂ = –3. 

The system has no solution when `a_1/a_2 = b_1/b_2 ≠ c_1/c_2` condition for parallel, distinct lines.

Compute: `a_1/a_2 = 1/2` 

`b_1/b_2 = 1/k` 

⇒ `1/2 = 1/k`

⇒ k = 2

Now check c-ratio: `c_1/c_2 = (-4)/(-3) = 4/3` and `1/2 ≠ 4/3`, so the inequality holds.

k = 2 will make the system have no solution.