Solve the following system of equation by elimination method.

3x + y = 8, 5x + y = 10

The given equations are

3x + y = 8 … (1)

5x + y = 10 … (2)

Here, the coefficients of y in both equations are numerically equal.

Subtracting (2) from (1),

⇒ (3x + y) – (5x + y) = 8 – 10

⇒ 3x + y – 5x – y = – 2

⇒ – 2x = – 2

⇒ x = 1

Substituting x = 1 in (1),

⇒ 3 (1) + y = 8

⇒ y = 8 – 3

⇒ y = 5

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