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4 September, 23:12

Solve the system of equations. y = 2x - 3 y = x^2 - 3

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  1. 4 September, 23:56
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    (0, - 3) and (2, 1)

    Step-by-step explanation:

    Given the 2 equations

    y = 2x - 3 → (1)

    y = x² - 3 → (2)

    Substitute y = x² - 3 into (1)

    x² - 3 = 2x - 3 (subtract 2x - 3 from both sides)

    x² - 2x = 0 ← factor out x from each term

    x (x - 2) = 0

    Equate each factor to zero and solve for x

    x = 0

    x - 2 = 0 ⇒ x = 2

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

    x = 0 : y = 2 (0) - 3 = 0 - 3 = - 3 ⇒ (0, - 3)

    x = 2 : y = 2 (2) - 3 = 4 - 3 = 1 ⇒ (2, 1)
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