Question

Find the value of k for which the system of equations x + 2y – 3 = 0 and 5x + ky + 7 = 0 is inconsistent.

Find k for which the system x + 2y = 3 and 5x + ky + 7 = 0 is inconsistent.

Answer 1

The given system is

x + 2y – 3 = 0   ...(i)

5x + ky + 7 = 0   ...(ii)

Here, a₁ = 1, b₁ = 2, c₁ = –3, a₂ = 5, b₂ = k and c₂ = 7.

For the system, to be inconsistent, we must have

`(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)`

⇒ `1/5 = 2/k ≠ (-3)/7`

⇒ `1/5 = 2/k`

⇒ k = 10

Hence, k = 10.