Question

If `[(x + y + z),(x + y),(y + z)] = [(7),(5),(3)]`, find the values of x, y and z.

Answer 1

Equate corresponding elements

x + y + z =  7   ...(i)

x + y = 5   ...(ii)

y + z = 3   ...(iii)

To find z

Subtract (ii) from (i):

(x + y + z) − (x + y) = 7 − 5

z = 2

To find y

Substitute z = 2 in equation (iii)

y + 2 = 3

y = 3 − 2

y = 1

To find x

Substitute y = 1 in equation (ii)

x + 1 = 5

x = 5 − 1

x = 4

Hence, x = 4, y = 1, z = 2.