Answer
$(6, -6)$
Work Step by Step
Given system is-
$-\frac{1}{3}x -\frac{1}{6}y$ = $-1$ __ eq.1
$\frac{2}{3}x +\frac{1}{6}y$ = $3$ __ eq.2
Adding eq.1 and eq.2 -
$-\frac{1}{3}x -\frac{1}{6}y+\frac{2}{3}x +\frac{1}{6}y$ = $-1+3$
i.e $-\frac{1}{3}x +\frac{2}{3}x $ = $2$
i.e.$-\frac{1}{3}x +\frac{2}{3}x $ = $2$
i.e.$x(-\frac{1}{3} +\frac{2}{3}) $ = $2$
i.e.$-\frac{1}{3}x +\frac{2}{3}x $ = $2$
i.e.$x(\frac{-1+2}{3} ) $ = $2$
i.e.$\frac{1}{3}x $ = $2$
i.e. $x$ = $2\times3$
i.e. $x$ = $6$
Substituting for $x$ in eq.2
$\frac{2}{3}(6) +\frac{1}{6}y$ = $3$
i.e. $4 +\frac{1}{6}y$ = $3$
i.e. $\frac{1}{6}y$ = $3-4$ = $-1$
i.e. $y$ = $-1\times6$
i.e. $y$ = $-6$
Thus $(6, -6)$ is the solution of given system.