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keigleyhannah30
01.09.2019 •
Mathematics
Solve the system of equations. y = x + 2, y = x2 + 7x + 10
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Ответ:
(- 2, 0 ) and (- 4, - 2 )
Step-by-step explanation:
Given the 2 equations
y = x + 2 → (1)
y = x² + 7x + 10 → (2)
Since both equations express y in terms of x we can equate them, that is
x² + 7x + 10 = x + 2 ( subtract x + 2 from both sides )
x² + 6x + 8 = 0 ← in standard form
(x + 2)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x + 4 = 0 ⇒ x = - 4
Substitute these values into (1) for corresponding values of y
x = - 2 : y = - 2 + 2 = 0 ⇒ (- 2, 0 )
x = - 4 : y = - 4 + 2 = - 2 ⇒ (- 4, - 2 )
Solutions are (- 2, 0 ) and (- 4, - 2 )
Ответ: