To solve this system of equations, we can use the method of elimination.
First, we can eliminate the variable y by adding the two equations together.
Adding the equations, we get:
2x - 2y + 3x + 2y = 6 + 9
Simplifying, we get:
5x = 15
Dividing both sides by 5, we get:
x = 3
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
2(3) - 2y = 6
Simplifying, we get:
6 - 2y = 6
Subtracting 6 from both sides, we get:
-2y = 0
Dividing both sides by -2, we get:
y = 0
Therefore, the solution to the system of equations is:
x = 3, y = 0
So the answer is B: x = 3, y = 0