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14 June, 04:57

Solve the following system of equations: y=6-x

y=x^2-6x+6

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Answers (1)
  1. 14 June, 05:02
    0
    (0, 6) and (5, 1)

    Step-by-step explanation:

    Given the 2 equations

    y = 6 - x → (1)

    y = x² - 6x + 6 → (2)

    Substitute y = x² - 6x + 6 into (1)

    x² - 6x + 6 = 6 - x (subtract 6 - x from both sides)

    x² - 5x = 0 ← factor out x from each term on the left side

    x (x - 5) = 0

    Equate each factor to zero and solve for x

    x = 0

    x - 5 = 0 ⇒ x = 5

    Substitute these values into (1) for corresponding value of y

    x = 0 : y = 6 - 0 = 6 ⇒ (0, 6)

    x = 5 : y = 6 - 5 = 1 ⇒ (5, 1)
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