Q22 of 186 Page 3

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

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 a2 = (2a – 1), b2 = (a – 1) and c2 = – (2a + 1)


For no solutions,



∴


On taking I and II terms, we get



⇒ 3(a – 1) = 2a – 1


⇒ 3a – 3 = 2a – 1


⇒ 3a – 2a = – 1 + 3


⇒ a = 2


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