Given:

Equation 1: kx – 5y = 2

Equation 2: 6x + 2y = 7

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 = k

a₂ = 6

b₁ = – 5

b₂ = 2

c₁ = 2

c₂ = 7

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

⇒ k ⇒ k = – 15

Also we find

The value of k for which the system of equations has no solution is k = – 15