Answer
$x=6$
$y=-10$
Work Step by Step
If we multiply the first equation by $\frac{3}{2}$, the second one by $\frac{2}{5}$, then we add the two equations, we can eliminate the $y$ from the system:
$-\frac{1}{3}\times \frac{3}{2}x+\frac{2}{5}\times \frac{3}{2}y=-6\times \frac{3}{2}$
$-\frac{1}{2}\times \frac{2}{5}x-\frac{3}{2}\frac{2}{5}y=12\times \frac{2}{5}$
$-\frac{1}{2}x-\frac{1}{5}x=-\frac{21}{5}$
$x=6$
$-\frac{1}{3}(6)+\frac{2}{5}y=-6$
$y=-10$
We have to check, if the solution is right. Substitute $x$ with 6 and $y$ with -10:
$-\frac{1}{3}(6)+\frac{2}{5}(-10)=-2-4=-6$ $\checkmark$
$-\frac{1}{2}(6)-\frac{3}{2}(-10)=-3+15=12$ $\checkmark$
