Exercise
What are the integer solutions of 14x + 6y = 0?
x = 6n, y = -14n, with n in Z
x = -3n, y = 7n, with n in Z
x = 7n, y = -3n, with n in Z
No, we also have x = -3 and y = 7 as a solution
Yes!
No, try n = 1 and find a counterexample