Question 1110336
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1.  Right sides are identical  ====>  hence, left sides are equal:

    x^3 = y^3.


2.  Since x and y are integer, the last equality implies  x = y.


3.  Then the either of the two given equations is equivalent to

    x^3 = 89x + 40x,   or

    x^3 = 129x,

    x*(x^2-129) = 0.


    In integer numbers, the last equation has only one solution  x= 0.



<U>Answer</U>.  The only solution to the original system in integer numbers is the pair (x,y) = (0,0).
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