set the two equations equal to each other:
x - 3 = -x - 1.
Adding x to both sides of the equation, we get:
2x - 3 = -1.
Adding 3 to both sides of the equation, we get:
2x = 2.
Dividing both sides of the equation by 2, we get:
x = 1.
Substituting x = 1 into one of the original equations, we find:
y = 1 - 3 = -2.
Therefore, the solution to the system is (x, y) = (1, -2).