Q12 of 39 Page 1

Find c if the system of equations cx + 3y + (3 – c) = 0 has 12x + cy – c = 0 has infinitely many solutions?

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

We know that if the system of equation a1x + b1y + c1 = 0

and a2x + b2y + c2 = 0 has infinitely many solution then

On comparing with given equations



Now,

⇒ c2 = 36 and 3(-c) = c(3 – c)

⇒ c = √36 and -3c = 3c - c2

⇒ c = ±6 and -3c - 3c  = - c2

⇒ c = ±6 and -6c = - c2

⇒ c = ±6 and c2 - 6c = 0

⇒ c = ±6 and c(c-6) = 0

⇒ c = -6,6 and c =0,6

Hence, at c = 6, the system of the equations have infinitely many solutions.


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