Question

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

2x - 3y = 7

(a + b)x - (a + b - 3)y = 4a + b

Answer 1

For infinitely many solution

⇒ 2a + 2b – 6 = 3a + 3b and 12a + 3b = 7a + 7b – 21

⇒ a + b = - 6 ----- (1)

and 5a – 4b = - 21 ------- (2)

Multiplying eq1 by 4 and adding to eq2

⇒ 9a = - 45

⇒ a = - 5

Thus, b = -1