Solve the system of equations. y = x + 2, y = x2 + 7x + 10

(- 2, 0 ) and (- 4, - 2 )

Step-by-step explanation:

Given the 2 equations

y = x + 2 → (1)

y = x² + 7x + 10 → (2)

Since both equations express y in terms of x we can equate them, that is

x² + 7x + 10 = x + 2 ( subtract x + 2 from both sides )

x² + 6x + 8 = 0 ← in standard form

(x + 2)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x + 4 = 0 ⇒ x = - 4

Substitute these values into (1) for corresponding values of y

x = - 2 : y = - 2 + 2 = 0 ⇒ (- 2, 0 )

x = - 4 : y = - 4 + 2 = - 2 ⇒ (- 4, - 2 )

Solutions are (- 2, 0 ) and (- 4, - 2 )

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