x + y = 3 x^2 + y^2 = 5 Solve

Question

x + y = 3
x^2 + y^2 = 5
Solve

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Euphemia 5 years 2021-07-17T15:09:10+00:00 2 Answers 15 views 0

Answers ( )

  1. King
    0
    2021-07-17T15:10:11+00:00
    Reply

    Answer:

    The solution doesn’t belong to the real numbers

  2. Acacia
    0
    2021-07-17T15:10:59+00:00
    Reply

    Answer:

    (1, 2 ), (2, 1 )

    Step-by-step explanation:

    Given the 2 equations

    x + y = 3 → (1)

    x² + y² = 5 → (2)

    Rearrange (1) expressing y in terms of x by subtracting x from both sides

    y = 3 – x → (3)

    Substitute y = 3 – x into (2)

    x² + (3 – x)² = 5 ← expand and simplify left side

    x² + 9 – 6x + x² = 5

    2x² – 6x + 9 = 5 ( subtract 5 from both sides )

    2x² – 6x + 4 ( divide through by 2 )

    x² – 3x + 2 = 0 ← in standard form

    (x – 1)(x – 2) = 0 ← in factored form

    Equate each factor to zero and solve for x

    x – 1 = 0 ⇒ x = 1

    x – 2 = 0 ⇒ x = 2

    Substitute these values into (3) for corresponding values of y

    x = 1 : y = 3 – 1 = 2 ⇒ (1, 2 )

    x = 2 : y = 3 – 2 = 1 ⇒ (2, 1 )

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