#### Answer

$x=4$
$y=-5$

#### Work Step by Step

If we multiply the first equation by $-2$ second equation by $3$, then we add the two equations, we can eliminate the $y$ from the system:
$4x\times(-2)+3\times(-2)y=1\times(-2)$
$3\times3x+2\times3y=2\times3$
$-8x+9x=4$
$x=4$
$4(4)+3y=1$
$y=-5$
We have to check, if the solution is right. Substitute $x$ with 4 and $y$ with -5:
$4(4)+3(-5)=1$ $\checkmark$
$3(4)+2(-5)=2$ $\checkmark$