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    jimbot's Avatar
    jimbot Posts: 2, Reputation: 1
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    #1

    Sep 16, 2009, 01:02 PM
    Substition or Elimination
    I have this problem that I can't solve:

    1/x + 1/y = 5/6
    1/x - 1/y = 1/6


    The book says the answer is (2,3)

    Please help.
    adam_89's Avatar
    adam_89 Posts: 1,866, Reputation: 280
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    #2

    Sep 16, 2009, 01:06 PM

    So you are to show how to solve for x & y?
    jimbot's Avatar
    jimbot Posts: 2, Reputation: 1
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    #3

    Sep 16, 2009, 01:08 PM
    Quote Originally Posted by adam_89 View Post
    So you are to show how to solve for x & y?
    Yes
    ArcSine's Avatar
    ArcSine Posts: 969, Reputation: 106
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    #4

    Sep 16, 2009, 02:42 PM
    Add the two equations together, which leaves you with an equation in x only. After solving that for x, plug your x-value result back into both original equations and solve for y, making sure that your results for y are consistent.
    morgaine300's Avatar
    morgaine300 Posts: 6,561, Reputation: 276
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    #5

    Sep 16, 2009, 10:02 PM

    In other words, use elimination. Note the y term is already a positive and negative of the same value, so you're all set to go. Don't let the fractions throw you off.

    (Doing substitution would just be icky.)
    KISS's Avatar
    KISS Posts: 12,510, Reputation: 839
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    #6

    Sep 16, 2009, 10:40 PM

    So, just adding the equations gives you 2/x = 1

    To make it look less icky, you can multiply top and bottom equations by 6 and add, but you can add 1/6 and 5/6 and you can subtract 1/y from 1/y and you can add 1/x and 1/x. The fractions should not intimidate you.
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