Given:

Equation 1: x + y = 4

Equation 2: 2x + ky = 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 no solutions we must have

………(i)

According to the problem:

a₁ = 1

a₂ = 2

b₁ = 1

b₂ = k

c₁ = 4

c₂ = 3

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

⇒ k = 2

Also we find

The value of k for which the system of equations has no solution is k = 2