Question

Solve for x and y:

`[(2, 5),(5, 2)][(x),(y)] = [(-7),(14)]`

Answer 1

`[(2, 5),(5, 2)][(x),(y)] = [(-7),(14)]`

`[(2x + 5y),(5x + 2y)] = [(-7),(14)]`

Comparing the corresponding elements, we get,

2x + 5y = –7  ...(1)

5x + 2y = 14  ...(2)

Multiplying (1) and 2 and (2) with 5, we get,

4x + 10y = –14  ...(3)

25x + 10y = 70  ...(4)

Subtracting (3) from (4), we get,

21x = 84

`=>` x = 4

From (2),

2y = 14 – 5x

= 14 – 20

= –6

`=>` y = –3