what are the solutions to the system?
y = x^2 + 3x - 4
y = 2x + 2
To find the solutions to the system, we need to set the equations equal to each other and solve for x:
x^2 + 3x - 4 = 2x + 2
By rearranging and factoring, we get:
x^2 + x - 6 = 0
(x + 3)(x - 2) = 0
Therefore, the solutions are x = -3 and x = 2. To find the corresponding y values, we can substitute each value of x into either of the original equations:
If x = -3, then y = (-3)^2 + 3(-3) - 4 = 2
If x = 2, then y = 2(2) + 2 = 6
So the solutions to the system are (-3, 2) and (2, 6).