Question

Solve the following systems of equations:

99x + 101y = 499

101x + 99y = 501

Answer 1

99x + 101y = 499

101x + 99y = 501

Adding both equations

⇒ 200x + 200y = 1000

⇒ x + y = 5 ------ (1)

Subtracting both equation

⇒ 2y – 2x = - 2

⇒ x – y = 1 ----- (2)

Adding 1 and 2

⇒ 2x = 6

⇒ x = 3

Thus,

3 + y = 5

⇒ y = 2