Question

Find the values of x and y from the following equation:

`((x - y, 2, -2),(4, x, 6)) + ((3, -2, 2),(1, 0, -1)) = ((6, 0, 0),(5, 2x + y, 5))`

Answer 1

We have,

`((x - y, 2, -2),(4, x, 6)) + ((3, -2, 2),(1, 0, -1)) = ((6, 0, 0),(5, 2x + y, 5))`

`(((x - y) + 3, 2 + (-2), -2 + 2),(4 + 1, x + 0, 6 + (-1))) = ((6, 0, 0),(5, 2x + y, 5))`

On comparing, we get

x − y + 3 = 6

x − y = 6 − 3

x − y = 3   ...(i)

and

x = 2x + y

x + y = 0   ...(ii)

Adding equations (i) and (ii)

(x − y) + (x + y) = 3 + 0

2x = 3

x = `3/2`

Substitute in x + y = 0

`3/2` + y = 0

y = `-3/2`