Show that set {(x,y) in Z | 5x+7y divisible by 3} is symmetric

[gummz]

Homework Statement

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

Show that S is symmetrical.

Homework Equations

None apart from basic algebraic knowledge.

The Attempt at a Solution

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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

 

[gummz]

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.