The sum of all three digit numbers is $(100+999)\cdot (\frac{900}{2})=1099 \cdot 450=494500$. So $600x+x+y=494500=601x+y$. To estimate $x$ we notice that $601x$ should be slightly less than $494500$. Thus $x<\frac{1099 \cdot 450}{601} \approx \frac{1100 \cdot 450}{600} = 825$, so $x$ is a little less than $825$. Testing some values gives us $x=822$ and $y=528$

The sum of all three digit numbers is $\frac{100+999}{2} \cdot 900 = 494550$. This means $494550-x-y=600x$, or $494550-y=601x$. We hence have $x = \left \lfloor \frac{494550}{601} \right \rfloor = 822$, so $y=528$.