Question

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

2x + 3y – 5 = 0, kx – 6y – 8 = 0

Answer 1

The given system of equations are

2x + 3y – 5 = 0

kx – 6y – 8 = 0

This system is of the form:

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

where, a₁ = 2, b₁ = 3, c₁ = –5 and a₂ = k, b₂ = –6, c₂ = –8

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

`(a_1)/(a_2) ≠ (b_1)/(b_2)`

⇒ `2/k ≠ 3/(-6)`

⇒ k ≠ –4

Hence, k ≠ –4