Q21 of 186 Page 3

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

(a – 1) x + 3y = 2, 6x + (1 – 2b) y = 6

Given, pair of equations


(a – 1)x + 3y = 2


and 6x + (1 – 2b)y = 6


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 – 1), b1 = 3 and c1 = – 2


and a2 = 6, b2 = 1 – 2b and c2 = – 6


For infinitely many solutions,


=


Here,


∴


On taking I and III terms, we get



⇒ 3(a – 1) = 6


⇒ 3a – 3 = 6


⇒ 3a = 6 + 3



On taking II and III terms, we get



⇒ 9 = 1 – 2b


⇒ – 2b = 9 – 1


⇒ – 2b = 8


⇒ b = – 4


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