#### Answer

$x =0$
$y=0$
$(0,0)$

#### Work Step by Step

$\frac{1}{2}x-\frac{1}{3}x=0$
$3x+2(y+5)=10$
Multiply the first equation by 6 to remove the fractions and simplify the second equation.
$6\times(\frac{1}{2}x)-6\times(\frac{1}{3}x)=0$ $\rightarrow$ $3x-2y=0$
$3x+2y +10=10$
Eliminate the $y$-variable by addition of the two equations.
$3x-2y+3x+2y+10=10$ $\rightarrow$ Simplify.
$6x=0$
$x=0$
Substitute for $x$ and solve for $y$.
$3(0)+2(y+5)=10$
$2y+10=10$
$2y=0$
$y=0$