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Solve by substitution (no wrong answers)​

Solve by substitution (no wrong answers)​-example-1

1 Answer

2 votes

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 )