Solve the following system of equation by elimination method.

65x – 33y = 97, 33x – 65y = 1

The given equations are

65x – 33y = 97 … (1)

33x – 65y = 1 … (2)

Adding (1) and (2),

⇒ 98x – 98y = 98

Dividing by 98,

⇒ x – y = 1 … (3)

Subtracting (1) and (2),

⇒ 32x + 32y = 96

Dividing by 32,

⇒ x + y = 3 … (4)

Solving (3) and (4),

⇒ x – y + (x + y) = 1 + 3

⇒ 2x = 4

⇒ x = 2

Substituting x = 2 in (4),

⇒ 2 + y = 3

⇒ y = 1

∴ (2, 1) is the solution to the given system.