Answer:
(- 4, 11 ) and (2, - 1 )
Step-by-step 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 )
