#### Answer

$x=\frac{1}{4}$
$y=-\frac{1}{2}$

#### Work Step by Step

If we multiply the second equation by $2$, then we add the two equations, we can eliminate the $y$ from the system:
$8x+4y=0$
$4\times2x-2\times2y=2\times2$
$8x+8x=4$
$16x=4$
$x=\frac{1}{4}$
$8\times\frac{1}{4}+4\times y=0$
$y=-\frac{1}{2}$
We have to check, if the solution is right. Substitute $x$ with $\frac{1}{4}$ and $y$ with $-\frac{1}{2}$:
$8(\frac{1}{4})+4(-\frac{1}{2})=0$ $\checkmark$
$4(\frac{1}{4})-2(-\frac{1}{2})=2$ $\checkmark$