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26 April, 20:32

Find the solution to the system

y=x^2+8x+2

y=7x+4

A (-2,-10) and (1,11)

B (2,10) and (-1,-11)

C (-2,-34) and (1,11)

D no solution

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Answers (1)
  1. 26 April, 20:49
    0
    A

    Step-by-step explanation:

    Given the 2 equations

    y = x² + 8x + 2 → (1)

    y = 7x + 4 → (2)

    Substitute y = x² + 8x + 2 into (2)

    x² + 8x + 2 = 7x + 4 (subtract 7x + 4 from both sides)

    x² + x - 2 = 0 ← in standard form

    (x + 2) (x - 1) = 0 ← in factored form

    Equate each factor to zero and solve for x

    x + 2 = 0 ⇒ x = - 2

    x - 1 = 0 ⇒ x = 1

    Substitute these values into (2) for the corresponding values of y

    x = - 2 : y = - 14 + 4 = - 10 ⇒ ( - 2, - 10)

    x = 1 : y = 7 + 4 = 11 ⇒ (1, 11)

    The solutions are ( - 2, - 10) and (1, 11) → A
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