solve linear-quadratic system algebraically. then what is the y-coordinate of the solution? show all work.

y = x^2 + 2x + 7
y – 7 = x

see explanation

Step-by-step explanation:

Given the 2 equations

y = x² + 2x + 7 → (1)

y - 7 = x → (2)

Rearrange (2) expressing y in terms of x by adding 7 to both sides

y = x + 7 → (3)

Substitute y = x + 7 into (1)

x + 7 = x² + 2x + 7 ( subtract x + 7 from both sides )

0 = x² + x ← factor out x from each term

0 = x(x + 1)

Equate each factor to zero and solve for x

x = 0

x + 1 = 0 ⇒ x = - 1

Substitute these values into (3) for corresponding values of y

x = 0 → y = 0 + 7 = 7

x = - 1 → y = - 1 + 7 = 6

The solutions are

(- 1, 6 ) and (0, 7 )

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step-by-step explanation:

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