Answer
$(\frac{-21}{10},\frac{3}{10})$
Work Step by Step
Given Equations,
$\frac{-x}{6} + \frac{y}{2} = \frac{1}{2}$ Equation $(1)$
$\frac{x}{3} - \frac{y}{6} = \frac{-3}{4}$ Equation $(2)$
Taking LCD, Multiply Equation $(1)$ by $6$ and multiply Equation $(2)$ by $12$
$6(\frac{-x}{6} + \frac{y}{2} )= 6(\frac{1}{2})$
$-x+3y=3$ Equation $(3)$
$12(\frac{x}{3} - \frac{y}{6}) = 12(\frac{-3}{4})$
$4x-2y=-9$ Equation $(4)$
From Equation $(3)$,
$-x+3y=3$
$-x=3-3y$
$x=3y-3$
Substituting $x$ in Equation $(4)$
$4x-2y=-9$
$4(3y-3)-2y=-9$
$12y-12-2y=-9$
$10y-12=-9$
$10y=-9+12$
$10y=3$
$y=\frac{3}{10}$
Substituting $y$ value in Equation $x=3y-3$ we get,
$x=3y-3$
$x=3(\frac{3}{10})-3$
$x=\frac{9}{10}-3$
$x=\frac{9-30}{10}$
$x=\frac{-21}{10}$
Solution: $(\frac{-21}{10},\frac{3}{10})$
