Answer
$x=0$
$y=-4$
Work Step by Step
If we add the two equations, we can eliminate the $x$ from the system:
$x-\frac{1}{2}y=2$
$-x+\frac{2}{5}y=-\frac{8}{5}$
$-\frac{1}{2}y+\frac{2}{5}y=\frac{2}{5}$
$x=0$
$0.4(0)+0.2y=0$
$y=-4$
$x-\frac{1}{2}(-4)=2$
$x=0$
We have to check, if the solution is right. Substitute $x$ with 0 and $y$ with -4:
$0-\frac{1}{2}(-4)=2$ $\checkmark$
$-0+\frac{2}{5}(-4)=-\frac{8}{5}$ $\checkmark$