#### Answer

$x=2$
$y=-3$

#### Work Step by Step

If we multiply the first equation by $-3$ second equation by $4$, then we add the two equations, we can eliminate the $y$ from the system:
$3x\times(-3)+4\times(-3)y=-6\times(-3)$
$5\times4x+3\times4y=1\times4$
$-9x+20x=22$
$x=2$
$3(2)+4y=-6$
$y=-3$
We have to check, if the solution is right. Substitute $x$ with 2 and $y$ with -3:
$3(2)+4(-3)=-6$ $\checkmark$
$5(2)+3(-3)=1$ $\checkmark$