Solve the following system of equation by elimination method.

13x + 11y = 70, 11x + 13y = 74

The given equations are

13x + 11y = 70 … (1)

11x + 13y = 74 … (2)

Adding (1) and (2),

⇒ 24x + 24y = 144

Dividing by 24,

⇒ x + y = 6 … (3)

Subtracting (2) from (1),

⇒ 2x + ( – 2y) = – 4

Dividing by 2,

⇒ x – y = – 4 … (4)

Solving (3) and (4),

⇒ x + y + (x – y) = 6 – 4

⇒ 2x = 2

⇒ x = 1

Substituting x = 1 in (3),

⇒ 1 + y = 6

⇒ y = 5

∴ (1, 5) is the solution to the given system.