Answer:
(4, - 11)
Explanation:
Given the 2 equations
y = x² - 2x - 19 → (1)
y + 4x = 5 → (2)
Rearrange (2) expressing y in terms of x by subtracting 4x from both sides
y = 5 - 4x → (3)
Substitute y = 5 - 4x into (1)
5 - 4x = x² - 2x - 19 ← subtract 5 - 4x from both sides
0 = x² + 2x - 24 ← in standard form
0 = (x + 6)(x - 4) ← in factored form
Equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 4 = 0 ⇒ x = 4
Substitute these values into (3) for corresponding values of y
x = - 6 : y = 5 + 24 = 29 ⇒ (6, 29)
x = 4 : y = 5 - 16 = - 11 ⇒ (4, - 11)