Answer
$x=4$
$y=3$
$(4,3)$
Work Step by Step
$\frac{1}{2}x+\frac{1}{3}y=3$ $(1)$
$\frac{1}{4}x-\frac{2}{3}y=-1$ $(2)$
Multiply Equation $(1)$ by 2
$x+\frac{2}{3}y=6$ $(1)$
$\frac{1}{4}x-\frac{2}{3}y=-1$ $(2)$
Add Equation $(1)$ from Equation $(2)$
$\frac{5}{4}x=5$
$x=4$
Substitute back to Equation $(2)$
$\frac{1}{4}(4)-\frac{2}{3}y=-1$
$1+1=\frac{2}{3}y$
$y=3$