Question

For what value of a, the following system of linear equations has no solutions:

3x + y = 1, (2a – 1) x + (a – 1) y = 2a + 1

Answer 1

Given, pair of equations

3x + y = 1

and (2a – 1)x + (a – 1)y = 2a + 1

On comparing the given equation with standard form i.e. a₁ x + b₁y + c₁ = 0 and a₂ x + b₂y + c₂ = 0, we get

a₁ = 3, b₁ = 1 and c₁ = – 1

and a_{2 =} (2a – 1), b₂ = (a – 1) and c₂ = – (2a + 1)

For no solutions,

⇒ 3(a – 1) = 2a – 1

⇒ 3a – 3 = 2a – 1

⇒ 3a – 2a = – 1 + 3

⇒ a = 2