Answer:
(- 4, 169 ) , (- 9, 414 )
Explanation:
y = - 49x - 27 → (1)
y = x² - 36x + 9 → (2)
substitute y = x² - 36x +9 into (1)
x² - 36x + 9 = - 49x - 27 ( add 49x to both sides )
x² + 13x + 9 = - 27 ( add 27 to both sides )
x² + 13x + 36 = 0 ← in standard form
(x + 4)(x + 9) = 0 ← in factored form
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x + 9 = 0 ⇒ x = - 9
substitute these values into (1) for corresponding values of y
x = - 4 : y = - 49(- 4) - 27 = 196 - 27 = 169 ⇒ (- 4, 169 )
x = - 9 : y = - 49(- 9) - 27 = 441 - 27 = 414 ⇒ (- 9, 414 )