Question

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

(k – 3) x + 3y – k, kx + ky - 12 = 0.

Answer 1

The given system of equations can be written as 

(k – 3) x + 3y - k = 0 

kx + ky - 12 = 0 

This system is of the form: 

a₁x+b₁y+c₁ = 0 a₂x+b₂y+c₂ = 0 

where, a₁ = k, b₁= 3, c₁ = -k and a₂ = k, b₂ = k, c₂ = -12 

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

⇒ k = 6 and k = ±6 

⇒ k = 6 

Hence, k = 6.