Find the values of a and b for which each of the following systems of linear equations has an infinite number of solutions:

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

Given: (2a - 1)x + 3y = 5 – eq 1

3x + (b - 1)y = 2 – eq 2

Here,

a₁ = (2a - 1), b₁ = 3, c₁ = - 5

a₂ = 3 , b₂ = (b - 1), c₂ = - 2

Given that system of equations has infinitely many solution

∴ = =

= =

Here,

=

- 2×(2a - 1) = 3×( - 5)

- 4a + 2 = - 15

- 4a = - 15 - 2

- 4a = - 17

b =

∴ b = -

Also,

=

3( - 2) = - 5×(b - 1)

- 6 = - 5b + 5

5b = 5 + 6

5b = 11

b =

∴b =

∴ a = , b =