Question

Find the solutions to the system. y = x2 – 2x –2 y = 4x + 5 (1 point) Responses (–1, 1) and (–7, –23) (–1, 1) and (–7, –23) (–1, 1) and (7, 33) (–1, 1) and (7, 33) (–1, 33) and (7, 1) (–1, 33) and (7, 1) no solution

Answer 1

First, set the two equations equal to each other:

x^2 - 2x - 2 = 4x + 5

Rearrange to put in standard form:

x^2 - 6x - 7 = 0

Factor or use the quadratic formula to find the solutions for x:

(x - 7)(x + 1) = 0

x = 7 or x = -1

Now, plug these values back into one of the original equations to find the corresponding y-values:

If x = -1,
y = (-1)^2 - 2(-1) - 2
y = 1 + 2 - 2
y = 1

If x = 7,
y = 7^2 - 2(7) - 2
y = 49 - 14 - 2
y = 33

So, the solutions to the system are (-1, 1) and (7, 33).