(2a – 1) x – 3y = 5, 3x + (b – 2) y = 3

Question

Find the values of a and b for which the following system of linear equations has infinitely many solutions:

(2a – 1) x – 3y = 5, 3x + (b – 2) y = 3

Answer 1

Given, pair of equations

(2a – 1)x – 3y = 5

and 3x + (b – 2)y = 3

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

a₁ = (2a – 1), b₁ = – 3 and c₁ = – 5

and a_{2 =} 3, b₂ = b – 2 and c₂ = 3

For infinitely many solutions,

⇒ 3(2a – 1) = 15

⇒ 6a – 3 = 15

⇒ 6a = 15 + 3

⇒ a = 18/6 = 3

On taking II and III terms, we get

⇒ -3/b - 2 = 5/3

⇒ – 9 = 5(b – 2)

⇒ 5b – 10 = – 9

⇒ 5b = – 9 + 10

⇒ b = 1/5