Solve the simultaneous equations 3 2x – y = 7 xy = 15

Question

Solve the simultaneous equations
3
2x – y = 7
xy = 15

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Thành Đạt 1 year 2021-08-23T12:19:15+00:00 1 Answers 23 views 0

Answers ( )

    0
    2021-08-23T12:21:05+00:00

    Answer:

    (5, 3 ) and (- \frac{3}{2}, – 10 )

    Step-by-step explanation:

    Given the 2 equations

    2x – y = 7 → (1)

    xy = 15 → (2)

    Rearrange (1) expressing y in terms of x , that is

    y = 2x – 7 → (3)

    Substitute y = 2x – 7 into (2)

    x(2x – 7) = 15

    2x² – 7x = 15 ( subtract 15 from both sides )

    2x² – 7x – 15 = 0 ← in standard form

    (x – 5)(2x + 3) = 0 ← in factored form

    Equate each factor to zero and solve for x

    x – 5 = 0 ⇒ x = 5

    2x + 3 = 0 ⇒ 2x = – 3 ⇒ x = – \frac{3}{2}

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

    x = 5 : y = 2(5) – 7 = 10 – 7 = 3 ⇒ (5, 3 )

    x = – \frac{3}{2} : y = 2(- \frac{3}{2} ) – 7 = – 3 – 7 = – 10 ⇒ (- \frac{3}{2}, – 10 )

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