Question

Question 127

Below u, v, w and x represent different integers, where u = (-4) and x $\ne$ 1. By using following equations, find each of the values $u\times v=u,x\times w=wandu+x=w$
(a) v
(b) w
(c) x
Expain your reason, using the properties of integers.

Answer 1

We have, three equations
$u\times v=u......\left(i\right)x\times w=w......\left(ii\right)u+x=w......\left(i\right)andu=-4$
(a) By putting the value of u in Eq. (i), we get
$(-4)\times v=(-4)\Rightarrow v=\frac{(-4)}{(-4)}\Rightarrow v=1$
(b) From Eq. (ii),
$x\times w=w\Rightarrow x=\frac{w}{w}\Rightarrow x=1But,x\ne 1$
Hence, $x\times w=w$ (ii) is possible, when w = 0 $(x\ne 1)$.
(c) From Eq. (iii), u + x = w
Put u = -4 and w=0, we get
$\Rightarrow -4+x=0\Rightarrow x=4\therefore v=1,x=4andw=0$