Try using the Substitution Method because the first equation is already in $y =$ form.

$5x − 3(−x − 2) = 22$
$5x + 3x + 6 = 22$
$8x + 6 = 22$
$8x + 6 − 6 = 22 − 6$
$8x = 16$
$x = 2$
Now substitute $2$ into either original equation for $x$ and solve for $y$.