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9 December, 16:16

Solve the system of equations. y = x + 2, y = x2 + 7x + 10

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  1. 9 December, 16:22
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    ( - 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)
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