Question

Solve the following systems of equations:

99x + 101y = 499
101x + 99y = 501

Answer 1

The given system of equation is

99x + 101y = 499      ...(i)

101x + 99y = 501    ...(ii)

Adding equation (i) and equation (ii), we get

99x + 101x + 101y + 99y = 499 + 501

⇒ 200x + 200y = 1000

⇒ 200(x + y) = 1000

⇒ `x + y = 1000/200 = 5`

⇒ x + y = 5            ...(iii)

Subtracting equation (i) by equation (ii), we get

101x − 99x + 99y − 101y = 501 − 499

⇒ 2x − 2y = 2

⇒ 2(x − y)  = 2

⇒ x − y = `2/2`

⇒ x − y = 1        ...(iv)

Adding equation (iii) and equation (iv), we get

2x = 5 + 1

⇒ `x = 6/2 = 3`

Putting x = 3 in equation (iii), we get

3 + y = 5

⇒ y = 5 − 3 = 2

Hence, solution of the given system of equation is x = 3, y = 2