Answer
$(6,0)$
Work Step by Step
Given Equations,
$\frac{x}{6} - \frac{y}{2} = 1$ Equation $(1)$
$\frac{x}{3} - \frac{y}{4} = 2$ Equation $(2)$
Taking LCD, Multiply Equation $(1)$ by $6$ and multiply Equation $(2)$ by $12$
$6(\frac{x}{6} - \frac{y}{2} )= 6(1)$
$x-3y=6$ Equation $(3)$
$12(\frac{x}{3} - \frac{y}{4} ) = 12(2)$
$4x-3y=24$ Equation $(4)$
From Equation $(3)$,
$x-3y=6$
$x=3y+6$
Substituting $x$ in Equation $(4)$
$4x-3y=24$
$4(3y+6)-3y=24$
$12y+24-3y=24$
$9y=24-24$
$9y=0$
$y=0$
Substituting $y$ value in Equation $x=3y+6$ we get,
$x=3y+6$
$x=3(0)+6$
$x=6$
Solution: $(6,0)$
