Question

If `[(xy, 4),(z + 6, x + y)] = [(8, w),(0, 6)]`, then find values of x, y, z and w.

Answer 1

Given that: `[(xy, 4),(z + 6, x + y)] = [(8, w),(0, 6)]`

Equating the corresponding elements,

xy = 8

w = 4

z + 6 = 0

⇒ z = – 6, x + y = 6

Now, solving x + y = 6  ......(i)

And xy = 8  .....(ii)

From equation (i), y = 6 – x   ......(iii)

Putting the value of y in equation (ii) we get,

x(6 – x) = 8

⇒ 6x – x² = 8

⇒ x² – 6x + 8 = 0

⇒ x² – 4x – 2x + 8 = 0

⇒ x(x – 4) – 2(x – 4) = 0

⇒ (x – 4) (x – 2) = 0

∴ x = 4, 2

From equation (iii)

y = 2, 4

Hence, x = 4 or 2, y = 2 or 4, z = – 6 and w = 4.