Answer
(6, -1)
Work Step by Step
Set the denominators equal to each other
$\frac{x + 2}{2} - \frac{y + 4}{3} = 3$
$\frac{3(x + 2)}{6} - \frac{2(y + 4)}{6} = \frac{18}{6}$
3(x + 2) - 2(y + 4) = 18
3x + 6 - 2y - 8 = 18
3x - 2y = 20
$\frac{x + y}{5} = \frac{x - y}{2} - \frac{5}{2}$
$\frac{2(x + y)}{10} = \frac{5(x - y)}{10} - \frac{25}{10}$
2(x + y) = 5(x - y) - 25
2x + 2y = 5x - 5y - 25
25 = 3x - 7y
25 = 3x - 7y can also be written as 3x = 25 + 7y
3x - 2y = 20 can also be written as 3x = 20 + 2y
Set them equal to one another
25 + 7y = 20 + 2y
5y = -5
y = -1
Plug y into 3x - 2y = 20
3x - 2(-1) = 20
3x + 2 = 20
3x = 18
x = 6
