ax + 3y = a – 2, 12x + ay = a

Question

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

ax + 3y = a – 2, 12x + ay = a

Answer 1

Given, pair of equations

ax + 3y = a – 2

and 12x + ay = a

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

a₁ = a, b₁ = 3 and c₁ = – (a – 2)

and a_{2 =} 12, b₂ = a and c₂ = – a

For no solutions,

⇒ a² = 36

⇒ a = √36

⇒ a = ±6