Answer
(8, -1)
Work Step by Step
Set the denominators equal to each other
$\frac{x-y}{3} = \frac{x + y}{2} - \frac{1}{2}$
$\frac{2(x-y)}{6} = \frac{3(x + y)}{6} - \frac{3}{6}$
2(x-y) = 3(x + y) - 3
2x - 2y = 3x + 3y - 3
-x = 5y - 3
x = -5y + 3
$\frac{x+2}{2} - 4 = \frac{y+4}{3}$
$\frac{3(x+2)}{6} - \frac{24}{6} = \frac{2(y+4)}{6}$
3(x+2) - 24 = 2(y+4)
3x + 6 - 24 = 2y + 8
3x - 2y = 26
Plug x = -5y + 3 into 3x - 2y = 26
3(-5y + 3) - 2y = 26
-15y + 9 - 2y = 26
-17y = 17
y = -1
Plug y into x = -5y + 3
x = -5(-1) + 3
x = 8
