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

From the second equation, we can rewrite it as y = x - 1.

Substitute y = x - 1 into the first equation:

x^2 - (x - 1) = 3
x^2 - x + 1 = 3
x^2 - x - 2 = 0
(x - 2)(x + 1) = 0

So, x = 2 or x = -1.

If x = 2, then y = 2 - 1 = 1. So, one solution is x = 2, y = 1.

If x = -1, then y = -1 - 1 = -2. So, another solution is x = -1, y = -2.

Therefore, the two solutions to the system of equations are: