Select the correct answer. What is the solution set of y= x2 + 2x + 7 and y=x+77
OA {(0,7),(-1, 6)}
O B. {(0,7), (-7, 0)}
OC. {(0,7), (1,8)}
D. {(-2, 0), (4,0)}

A

Step-by-step explanation:

Given the 2 equations

y = x² + 2x + 7 → (1)

y = x + 7 → (2)

Substitute y = x² + 2x + 7 into (2)

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

x² + x = 0 ← factor out x from each term on the left side

x(x + 1) = 0

Equate each factor to zero and solve for x

x = 0

x + 1 = 0 ⇒ x = - 1

Substitute these values into (2) for corresponding values of y

x = 0 → y = 0 + 7 = 7 ⇒ (0, 7 )

x = - 1 → y = - 1 + 7 = 6 ⇒ (- 1, 6 )

take it another