Solve for x and y:

We are given with a matrix equation,

We need to find x and y.

These matrices can be added easily as they are of same order.

If two matrices are equal, then their corresponding elements are also equal.

This implies,

2x + 3y – 8 = 0 …(i)

x + 5y – 11 = 0 …(ii)

We have two variables, x and y; and two equations. It can be solved.

Rearranging equation (i), we get

2x + 3y = 8 …(iii)

Rearranging equation (ii), then multiplying it by 2 on both sides, we get

x + 5y = 11

2(x + 5y) = 2 × 11

⇒ 2x + 10y = 22 …(iv)

Subtracting equation (iii) from (iv), we get

(2x + 10y) – (2x + 3y) = 22 – 8

⇒ 2x + 10y – 2x – 3y = 14

⇒ 2x – 2x + 10y – 3y = 14

⇒ 7y = 14

⇒ y = 2

Substituting y = 2 in equation (iii), we get

2x + 3(2) = 8

⇒ 2x + 6 = 8

⇒ 2x = 8 – 6

⇒ 2x = 2

⇒ x = 1

Thus, x = 1 and y = 2.