What are the solutions to the system? which is the true correct answer and why

y = x2 + 3x – 4
y = 2x + 2
(1 point)
Responses

(–3, 6) and (2, –4)
(–3, 6) and (2, –4)

(–3, –4) and (2, 6)
(–3, –4) and (2, 6)

(–3, –4) and (–2, –2)
(–3, –4) and (–2, –2)

no solution

1 answer

The correct solution is (-3, -4) and (2, 6).

To find the solutions, we can set the two equations equal to each other:
x^2 + 3x - 4 = 2x + 2
x^2 + x - 6 = 0
(x + 3)(x - 2) = 0
x = -3 or x = 2

Plugging the values of x back into the second equation y = 2x + 2:
For x = -3, y = 2(-3) + 2 = -4
For x = 2, y = 2(2) + 2 = 6

Therefore, the solutions to the system are (-3, -4) and (2, 6).