Assume contradiction. Square both equations and sum them up. Because of Jacobi's four square theorem we will have contradiction with non-zero integer condition.

electrovector wrote: Square both equations and sum them up. $(a^2+b^2)(x^2+y^2)=257$ But 257 is prime.

257 is prime.

Solution: If we get the square of eguations and add them to each other we will gain (a^2 +b^2)(x^2+y^2)=257 but 257 is prime