Answer
$x=-1$
$y=-\frac{1}{2}$
(-1,$-\frac{1}{2}$)
Work Step by Step
$\frac{3}{4}x-\frac{y}{2}=-\frac{1}{2}$
$x+y=-\frac{3}{2}$
Remove fractions.
Multiply both sides of the first equation by 4.
$4(\frac{3}{4}x-\frac{y}{2})=4(-\frac{1}{2})\longrightarrow$ Simplify. Apply the distributive property.
$3x-2y=-2$
Multiply both sides of the second equation by 2.
$2(x+y)=2(-\frac{3}{2})\longrightarrow$ Simplify. Apply the distributive property.
$2x+2y=-3$
Add the two new equations together to eliminate y.
$3x-2y=-2$
$\underline{2x+2y=-3}$
$5x\ \ \ \ \ \ \ \ \ =-5$
Solve for x.
$5x=-5\longrightarrow$ Divide both sides by 5.
$5x\div5=-5\div5\longrightarrow$ Simplify.
$x=-1$
Substitute for x in any equation to solve for y.
$-1+y=-\frac{3}{2}\longrightarrow$ Add 1 to both sides.
$-1+y+1=-\frac{3}{2}+1\longrightarrow$ Simplify.
$y=-\frac{1}{2}$