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. a_{1} x + b_{1}y + c_{1} = 0 and a_{2} x + b_{2}y + c_{2} = 0, we get

a_{1} = c, b_{1} = 3 and c_{1} = – (c – 3)

and a_{2 =} 12, b_{2} = c and c_{2} = – c

For infinitely many solutions,

Here,

∴ …(1)

On taking I and III terms, we get

⇒ c^{2} = 36

⇒ c = √36

⇒ c = ±6

But c = – 6 not satisfies the eq^{n} (1)

Hence, the required value of c = 6.

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