Question

Find the value of k for which the following system of equations has a unique solution:

4x + ky + 8 = 0, x + y + 1 = 0

Answer 1

The given system of equations is

4x + ky + 8 = 0

x + y + 1 = 0

This system is of the form:

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

where, a₁ = 4, b₁ = k, c₁ = 8 and a₂ = 1, b₂ = 1, c₂ = 1

For the given system of equations to have a unique solution, we must have:

`(a_1)/(a_2) ≠ (b_1)/(b_2)`

⇒ `4/1 ≠ k/1`

⇒ k ≠ 4

Hence, k ≠ 4.