Question

Find the value of x and y if (2x + y, x + 2y) = (5, 4).

Answer 1

Given: 2x + y = 5, x + 2y = 4

Step-wise calculation:

1. Multiply the first equation by 2:

4x + 2y = 10

2. Subtract the second equation:

(4x + 2y) – (x + 2y) = 10 – 4

⇒ 3x = 6

⇒ x = 2

3. Substitute x = 2 into 2x + y = 5

⇒ 2(2) + y = 5

⇒ 4 + y = 5

⇒ y = 1

⇒ x = 2, y = 1