Answer
$(-\frac{1}{a-1}, \frac{1}{a-1})$
Work Step by Step
Given system is-
$x +y$ = $0$
i.e. $x $ = $-y$ __ eq.1
$x +ay$ = $1$ __ eq.2
Substituting for $x$ in eq.2 from eq.1
$-y+ay$ = $1$
i.e. $ay-y$ = $1$
i.e. $y(a-1)$ = $1$
i.e. $y$ = $\frac{1}{a-1}$
Substituting for $y$ in eq.1
$x $ = $-y$
$x $ = $-\frac{1}{a-1}$
Thus $(-\frac{1}{a-1}, \frac{1}{a-1})$ is the solution of given system.
