What are the solutions to the system of equations? { Y=2x^2-6x+3 { y=x-2

Question

What are the solutions to the system of equations?
{ Y=2x^2-6x+3
{ y=x-2

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Jade 2 weeks 2021-09-10T22:28:51+00:00 2 Answers 0

Answers ( )

    0
    2021-09-10T22:30:13+00:00

    Answer:

    see explanation

    Step-by-step explanation:

    Given the 2 equations

    y = 2x² – 6x + 3 → (1)

    y = x – 2 → (2)

    Since both equations express y in terms of x we can equate the right sides, that is

    2x² – 6x + 3 = x – 2 ( subtract x – 2 from both sides )

    2x² – 7x + 5 = 0 ← in standard form

    Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

    product = 2 × 5 = 10 and sum = – 7

    The factors are – 2 and – 5

    Use these factors to split the x- term

    2x² – 2x – 5x + 5 = 0 ( factor the first/second and third/fourth terms )

    2x(x – 1) – 5(x – 1) = 0 ← factor out (x – 1) from each term

    (x – 1)(2x – 5) = 0

    Equate each factor to zero and solve for x

    x – 1 = 0 ⇒ x = 1

    2x – 5 = 0 ⇒ 2x = 5 ⇒ x = \frac{5}{2}

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

    x = 1 : y = 1 – 2 = – 1 ⇒ (1, – 1)

    x = \frac{5}{2} : y = \frac{5}{2} – 2 = \frac{1}{2}

    Solutions are (1, – 1) and ( \frac{5}{2}, \frac{1}{2} )

    0
    2021-09-10T22:30:33+00:00

    Answer:

    Step-by-step explanation:

    x=1, y=-1

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