Question

Below u, v, w and x represent different integers, where u = –4 and x ≠ 1. By using following equations, find each of the values:
u × v = u
x × w = w
u + x = w

1. v
2. w
3. x

Explain your reasoning using the properties of integers.

Answer 1

We have, three equations

u × v = u  ......(i)

x × w = w  ......(ii)

u + x = w  ......(iii)

and u = –4

a. By putting the value of u in equation (i), we get

(–4) × v = (–4)

⇒ v = `((-4))/((-4))`

⇒ v = 1

b. From equation (ii),

x × w = w

⇒ x = `w/w`

⇒ v = 1

But, Hence x × w = w, (ii) is possible, when w = 0 (x ≠ 1).

c. From equation (iii), u + x = w

Put u = –4 and w = 0, we get

⇒ –4 + x = 0

⇒ x = 4

∴ v = 1, x = 4 and w = 0.