The value of k for which the system of equations x + 2y – 3 = 0 and 5x + ky + 7 = 0 has no solution, is

Given:

Equation 1: x + 2y = 3

Equation 2: 5x + ky = – 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 = 1

a₂ = 5

b₁ = 2

b₂ = k

c₁ = 3

c₂ = – 7

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

⇒ k = 10

Also we find

The value of k for which the system of equations has no solution is k = 10