Question

Solve the system of equations.
y = x2 - 5
y = -2x + 3

Answer 1

(- 4, 11 ) and (2, - 1 )

Explanation:

Given the 2 equations

y = x² - 5 → (1)

y = - 2x + 3 → (2)

Substitute y = x² - 5 into (2)

x² - 5 = - 2x + 3 ( subtract 2x + 3 from both sides )

x² + 2x - 8 = 0 ← in standard form

(x + 4)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

Substitute these values into either of the 2 equations for corresponding values of y.

Substituting into (2)

x = - 4 : y = - 2(- 4) + 3 = 8 + 3 = 11 ⇒ (- 4, 11 )

x = 2 : y = - 2(2) + 3 = - 4 + 3 = - 1 ⇒ (2, - 1 )