The value of k for which the system of equations

kx – y = 2

6x – 2y = 3

has a unique solution, is

Given:

Equation 1: kx – y = 2

Equation 2: 6x – 2y = 3

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

For the system of linear equations to have unique solution we must have

………(i)

According to the problem:

a₁ = k

a₂ = 6

b₁ = – 1

b₂ = – 2

c₁ = 2

c₂ = 3

Putting the above values in equation (i) we get

⇒ k ≠ ⇒ k ≠ 3

The value of k for which the system of equations has unique solution is k≠3