Question

Find the values of p and q for which the following system of linear equations has infinite number of solutions:

2x + 3y = 9

(p + q)x - (2p - q)y = 3(p + q + 1)

Answer 1

For infinitely many solution

⇒ - 4p + 2q = 3p + 3q and 2p + 2q + 2 = 9p + 9q

⇒ q = - 7p and 7p + 7q = 2

⇒ 7q – q = 2

⇒ q = 1/3

Thus, p = -1/21