Given:

Equation 1: 2x – y = 5

Equation 2: 6x + ky = 15

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 infinitely many solutions we must have

………(i)

According to the problem:

a₁ = 2

a₂ = 6

b₁ = – 1

b₂ = k

c₁ = 5

c₂ = 15

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

⇒ 2k = – 6 ⇒ k = – 3

Also we find

The value of k for which the system of equations has infinitely many solution is k = – 3