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

First, let's write the two equations together:

5x - 2y = 9
7x + 2y = 3

Now, add the two equations together to eliminate y:

5x - 2y + 7x + 2y = 9 + 3
12x = 12
x = 1

Next, substitute x back into one of the equations to solve for y. Let's use the first equation:

5(1) - 2y = 9
5 - 2y = 9
-2y = 4
y = -2

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