Answer
$x=0$
$y=3$
Work Step by Step
If we multiply the second equation by $-3$, then we add the two equations, we can eliminate the $y$ from the system:
$\frac{3}{2}x+y=3$
$\frac{2}{3}\times (-3)x+\frac{1}{3}\times(-3)y=1\times (-3)$
$\frac{3}{2}x-2x=0$
$x=0$
$\frac{3}{2}(0)+y=3$
$y=3$
We have to check, if the solution is right. Substitute $x$ with 0 and $y$ with 3:
$\frac{3}{2}(0)+3=3$ $\checkmark$
$\frac{2}{3}(0)+\frac{1}{3}(3)=1$ $\checkmark$