Question

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 1

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 a_{2 =} 12, b₂ = c and c₂ = – c

For infinitely many solutions,

⇒ c² = 36

⇒ c = √36

⇒ c = ±6

But c = – 6 not satisfies the eqⁿ (1)

Hence, the required value of c = 6.