How to calculate concentrations when dissolving two salts?


> 
> Some solid silver bromate was dissolved together with solid silver acetate what would be the highest achievable pH?
>  \begin{align}
> K\_\mathrm{sp}(\ce{AgBrO3}) &= 5.38 \times 10^{-5}\\
> K\_\mathrm{sp}(\ce{AgCH3COO}) &= 1.94 \times 10^{-3}\\
> \mathrm{p}K\_\mathrm{a}(\ce{CH3COOH}) &= 4.76
> \end{align}
> 
> 
> 


Now I know this is just a question about the common ion effect. I know how to do the question if silver ions are already present in the solution then silver acetate is added. Also given the concentration of acetate ions, I can easily calculate the pH.


The real problem with this question is that you are dissolving 2 salts which are **both in equilibrium**. I don't know how to calculate the concentration of acetate ions in this scenario. 


This is what I did:


$$5.38 \times 10^{-5} = [\ce{Ag+}][\ce{BrO3-}] = x^2$$
$$x = \ce{[Ag+]} = 7.33 \times 10^{-3}$$
$$1.94 \times 10^{-3} = [\ce{Ag+}][\ce{CH3COO}] = (7.33 \times 10^{-3} + y)(y)$$
I then used quadratic formula to find y.


I am pretty sure that this method is wrong because wouldn't the dissolution of silver acetate cause the equilibrium of silver bromate to shift backwards, causing the value of x to decrease. Or can we assume that this shift is negligible. 


Also, by **highest achievable pH** doesn't that imply that the final pH of solution is variable. However, shouldn't it have the same pH every single time, making the words *highest achievable pH* redundant? Or am I missing something? 


