To solve for x and y in this system of equations, we can use the method of substitution or elimination.

Given equations:
1) 5x + 3y = 2y
2) 3x - 2y = 24

Let's solve by substitution:
From equation 1, we can rearrange it to solve for x:
5x + 3y = 2y
5x = -y
x = -y/5

Now, substitute x in equation 2:
3(-y/5) - 2y = 24
-3y/5 - 2y = 24
-3y - 10y = 120
-13y = 120
y = -120/13

Now that we have found the value of y, we can substitute it back into the equation x = -y/5:
x = -(-120/13) / 5
x = 24/13

Therefore, the solutions to the system of equations are:
x = 24/13
y = -120/13