My friend gave me this problem which I have not been able to solve:

> 
> Let $S(k)$ denote the sum of the digits of $k$. Find all natural solutions $(x,y,z)$ to the equations:
> 
> 
> $S(x) + S(y) + S(z) = y-4$
> 
> 
> $S(x) + S(y) = x$
> 
> 
> $x + y + S(z) = z$
> 
> 
> 

Any help in solving this(I would like to have some hints)?

Edit: Solutions are ok too please.