Answer
$x=\frac{3}{2}$
$y=-\frac{3}{2}$
Work Step by Step
If we multiply the first equation by $-2$, the second one by $3$, then we add the two equations, we can eliminate the $y$ from the system:
$3\times(-2)x+3\times(-2)y=0\times(-2)$
$4\times3x+2\times3y=3\times3$
$-6x+12x=9$
$x=\frac{3}{2}$
$3\times\frac{3}{2}+3\times y=0$
$y=-\frac{3}{2}$
We have to check, if the solution is right. Substitute $x$ with $\frac{3}{2}$ and $y$ with $-\frac{3}{2}$:
$3(\frac{3}{2})+3(-\frac{3}{2})=0$ $\checkmark$
$4(\frac{3}{2})+2(-\frac{3}{2})=3$ $\checkmark$
