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 = 
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