Q23 of 186 Page 3

For what value of c, the following system of linear equations has infinite number of solutions:

2x + 3y = 2, (c + 2) x + (2c + 1) y = 2 (c – 1)

Given, pair of equations


2x + 3y = 2


and (c + 2)x + (2c + 1)y = 2(c – 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 = 2, b1 = 3 and c1 = – 2


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


For infinitely many solutions,



Here,


…(1)


On taking I and III terms, we get



⇒ 2(2c + 1) = 3(c + 2)


⇒ 4c + 2 = 3c + 6


⇒ 4c – 3c = 6 – 2


⇒ c = 4


Hence, the required value of c = 4.


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