diven8765
24.05.2020 •
Mathematics
A system of equations is given.
y= x^2 −9
y= −2x−1
What is one solution to the system of equations?
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Ответ:
(- 4, 7 ) and (2, - 5 )
Step-by-step explanation:
Given the 2 equations
y = x² - 9 → (1)
y = - 2x - 1 → (2)
Substitute y = x² - 9 into (2)
x² - 9 = - 2x - 1 ( subtract - 2x - 1 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 (2) for corresponding values of y
x = - 4 → y = - 2(- 4) - 1 = 8 - 1 = 7 ⇒ (- 4, 7 )
x = 2 → y = - 2(2) - 1 = - 4 - 1 = - 5 ⇒ (2, - 5 )
Ответ: