prove that x and y are even if 5x + y = 8

Question

I have to prove that x and y are even if 5x + y = 8

Answer 1

Let's see. If x=1, then y = 3.  
That disproves the assertion.

 

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Answer 2

5x + y = 8

 

y = -5x + 8

 

Here is a counterexample:

 

x = 1

y = -5(1) + 8 = 3

 

Both x and y are odd in this example, showing that the proposition that you are trying to prove is not always true.