To solve this system of equations, we can use the method of elimination.

First, let's add the two equations together to eliminate the variable y:
(2x - y) + (3x + y) = 3 + 7
5x = 10
Dividing both sides by 5, we get:
x = 2

Now, substitute this value of x back into one of the original equations to solve for y. Let's use the second equation:
3(2) + y = 7
6 + y = 7
Subtracting 6 from both sides, we get:
y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.