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Homework Help: System of two equations with fractions

  1. May 23, 2013 #1
    1. The problem statement, all variables and given/known data

    These are the two equations:

    (7 + x)/5 - (2x - y)/4 - 3y = -5
    (5y - 7)/2 - (4x - 3)/6 - 18 = -5x

    2. Relevant equations

    3. The attempt at a solution

    When I try to simplify it, I end up with:

    6x + 55y = 128
    34x + 15y = 129

    I'm not sure where to go with this, I think I should have gone a different route instead of just trying to simplify the equations.Does anyone know where I might have gone wrong?
    By the way, in the answers of the book it says that X is 3 and Y is 2, however I must find them by solving the problem, but I am stuck.Any help would be appreciated.
  2. jcsd
  3. May 23, 2013 #2


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    Are you sure you've stated the problem correctly? The second one is perhaps = -6x on the right?
    Have you not been shown how to solve simultaneous equations? It's very easy. One way is to write one of the equations in the form y = (some expression with x and constants but no y's), then use that to replace y in the other equation.
  4. May 23, 2013 #3
    Yeah thanks, but it seems like the problem is wrong, the second equation doesn't add up with the answer they've given, even when I calculate it with software.
  5. May 23, 2013 #4

    Ray Vickson

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    The solution of your two equations (exactly as written) is x = 501/134, y = 643/335. Are you sure you wrote the correct equations?

    BTW: when I (or, actually, Maple 14) simplify your equations I get
    [tex]6x + 55y = 128\\
    26x + 15y = 126[/tex]
    and these also give the values of x and y as stated above.
  6. May 23, 2013 #5


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    Check your arithmetic on both equations.
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