Question

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

x – ky = 2, 3x + 2y + 5 = 0

Answer 1

The given system of equations are

x – ky – 2 = 0

3x + 2y + 5 = 0

This system of equations is of the form:

a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0

where, a₁ = 1, b₁ = –k, c₁ = –2 and a₂ = 3, b₂ = 2, c₂ = 5

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

`(a_1)/(a_2) ≠ (b_1)/(b_2)`

⇒ `1/3 ≠ -k/2`

⇒ `k ≠ -2/3`

Hence, `k ≠ -2/3`