Given:

Equation 1: x + ky = 0

Equation 2: 2x – y = 0

Both the equations are in the form of :

a₁x + b₁y = c₁ & a₂x + b₂y = c₂ where

a₁ & a₂ are the coefficients of x

b₁ & b₂ are the coefficients of y

c₁ & c₂ are the constants

According to the problem:

a₁ = 1

a₂ = 2

b₁ = k

b₂ = – 1

c₁ = 0

c₂ = 0

So for this problem the system of linear equations will have unique solution if

.......(i)

Putting the above values in equation (i) we get:

⇒ k≠

The value of k for which the system of equations has unique solution is k≠