Solve the following system of equations and show all work. y = x^2 + 3 y = x + 5 (10 points)

(- 1, 4 ) and (2, 7 )

Step-by-step explanation:

Given the 2 equations

y = x² + 3 → (1)

y = x + 5 → (2)

Substitute y = x² + 3 into (2)

x² + 3 = x + 5 ← subtract x + 5 from both sides

x² - x - 2 = 0 ← in standard form

(x - 2)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x + 1 = 0 ⇒ x = - 1

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

x = 2 : y = 2 + 5 = 7 ⇒ (2, 7 )

x = - 1 : y = - 1 + 5 = 4 ⇒ (- 1, 4 )