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Show symmetry in a (x,y) | 3a=f(x,y) set

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data

    Let S = { (x,y) in Z | 5x+7y is divisible by 3 }

    Show that S is symmetrical.

    2. Relevant equations

    None apart from basic algebraic knowledge.

    3. The attempt at a solution

    The only thing I can think of is starting with 3a = 5x+7y and putting x (or y) into the corresponding number 5y+7x and show that that turns out to be a multiple of 3, to show that it is symmetrical. But that leads me nowhere as far as I can tell:

    5y+7x = 5y + 7 * (3a-7y) / 5
     
  2. jcsd
  3. Oct 26, 2014 #2
    Nevermind, I got it:

    5y+7x = 5x+7y + (2x-2y) and you isolate 2x-2y from the given 3a equation. Now this is a multiple of 3.
     
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