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Math

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Hi. So we had a long test with this question.. I was wondering how to solve it? Coz our teacher didn't discuss the answers.. and most probably we'll have the same type of question during midterms..

Find the Solution Set

9/|2-5x| - 4/y^2-3y = 5
2/|2-5x| + 2/ 3(y^2-3y) = 1/3


thanks!

  • Math -

    I think I would eliminate variables.

    multiply the first equation by 2/3
    multiply the second equation by 4

    add the equations.

    solve for abs(2-5x), you will have two solutions.

    Then, put each of those solutions into the first equation, and solve for y.

    Get a large blank pad on which to do this problem, and check it twice. You can finally check each solution by substitution into the second equation.

  • Math -

    That's quite nasty for a test.

    I would try the following, along the lines suggested by bobpursley

    multiply the first by 2
    18/|2-5x| - 8/(y^2-3y) = 10
    multiply the second by 9
    18/|2-5x| + 6/(y^2-3y) = 3
    subtract:
    -14/(y^2-3y) = 7
    7y^2 - 21y + 14 = 0
    y^2 - 3y + 2 = 0
    (y-2)(y-1) = 0
    y = 2 or y = 1

    I will do the y=2

    If y = 2 , then
    9/|2-5x| - 4/-2 = 5
    9/|2-5x| = 3
    3/|2-5x| = 1
    |2-5x| = 3

    case1: 2-5x=3
    -5x = 1
    x = -1/5

    case2:
    -2 + 5x = 3
    5x = 5
    x = 1

    so two pairs from that part:
    (1,2) and (-1/5, 2)

    you do the other two solutions, using y = 1

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