Q. 23 A5.0( 2 Votes )

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

cx + 3y – (c – 3) = 0, 12x + cy – c = 0

Answer :

Given, pair of equations


cx + 3y – (c – 3) = 0


and 12x + cy – c = 0


On comparing the given equation with standard form i.e. a1 x + b1y + c1 = 0 and a2 x + b2y + c2 = 0, we get


a1 = c, b1 = 3 and c1 = – (c – 3)


and a2 = 12, b2 = c and c2 = – c


For infinitely many solutions,



Here,


…(1)


On taking I and III terms, we get



c2 = 36


c = √36


c = ±6


But c = – 6 not satisfies the eqn (1)


Hence, the required value of c = 6.


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