Question

Find the values of x, y, z if `[(2x + y, x - y),(x - z, x + y + z)] = [(10, -1),(2, 8)]`.

Answer 1

Equate corresponding elements

2x + y = 10   ...(i)

x − y = −1   ...(ii)

x − z = 2   ...(iii)

x + y + z = 8   ...(iv)

To find x and y

Add equations (i) and (ii)

(2x + y) + (x − y) = 10 + (−1)

3x = 9

x = `9/3`

x = 3

Substitute x = 3 in equation (ii)

3 − y = −1

−y = −1 − 3

−y = −4

y = 4

To find z

Substitute x = 3 in equation (iii)

3 − z = 2

−z = 2 − 3

−z = −1

z = 1

Check with equation (iv)

x + y + z

= 3 + 4 + 1

= 8

Hence, x = 3, y = 4, z = 1.