Answer
$$x=8$$ $$y=-6$$
Work Step by Step
equation 1 $$\frac{3}{4}x+\frac{2}{3}y=2$$ equation 2 $$x+\frac{y}{3}=6$$
Multiply equation 2 by $-2$:
$$[x+\frac{y}{3}=6]\cdot-2$$ $$-2x-\frac{2}{3}y=-12$$
Add this to equation 1:
$$\frac{3}{4}x+\frac{2}{3}y=2$$ $$-2x-\frac{2}{3}y=-12$$ $$-\frac{5}{4}x=-10$$ $$-5x=-40$$ $$x=8$$
Substitute this value of $x$ to equation 2:
$$x+\frac{y}{3}=6$$ $$8+\frac{y}{3}=6$$ $$\frac{y}{3}=6-8$$ $$\frac{y}{3}=-2$$ $$y=-6$$
