Answer
The solution is
$ x=6 $ and $ y=10 $.
Work Step by Step
The given equations are
$ \frac{2x}{3}+\frac{y}{5}=6 $ ... (1)
$ \frac{x}{6}-\frac{y}{2}=-4 $ ... (2)
Multiply equation (1) by $ 5$ and equation (2) by $2 $.
$ \frac{10x}{3}+y=30 $ ... (3)
$ \frac{x}{3}-y=-8 $ ... (4)
Add equation (3) and (4).
$ \frac{10x}{3}+\frac{x}{3}=30-8 $
$ \frac{10x+x}{3}=22 $
$ \frac{11x}{3}=22 $
$ x=22\cdot \frac{3}{11} $
$ x=6 $ substitute into equation (4)
$ \frac{6}{3}-y=-8 $
$ 2-y=-8 $
$2+8=y $
$ 10=y $
