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2 June, 08:24

Use the substitution and to rewrite the equations in the system in terms of the variables and. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original system in terms of x and y.

-3/x+4/y=11

1/x-2/y=-5

+5
Answers (1)
  1. 2 June, 08:48
    0
    x = - 1 and y = 1/2

    Step-by-step explanation:

    Let u = 1/x, and v = 1/y

    Then the pair of equations

    -3/x + 4/y = 11

    1/x - 2/y = - 5

    Can be written as

    -3u + 4v = 11 ... (1)

    u - 2v = - 5 ... (2)

    From (2)

    u = 2v - 5 ... (3)

    Substituting (3) into (1)

    -3 (2v - 5) + 4v = 11

    -6v + 15 + 4v = 11

    -6v + 4v = 11 - 15

    -2v = - 4

    v = 4/2 = 2

    Substituting this value of v in (3)

    u = 2v - 5

    u = 2 (2) - 5

    = 4 - 5

    = - 1

    That is

    u = - 1, v = 2

    Since u = 1/x, and v = 1/y, we have

    1/x = - 1

    => x = - 1

    And

    1/y = 2

    => y = 1/2

    Therefore

    x = - 1 and y = 1/2
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