Question

The pair of equations λx + 3y = 7, 2x + 6y = 14 will have infinitely many solutions for λ = ______.

Answer 1

The pair of equations λx + 3y = 7, 2x + 6y = 14 will have infinitely many solutions for λ = 1.

Explanation:

For infinitely many solutions the two equations must be proportional.

So (λ, 3, 7) must be proportional to (2, 6, 14).

Thus `λ/2 = 3/6 = 7/14 = 1/2`, giving λ = 1.