We have the utility function $$U(x,y)=x + y$$ and we have to derive the substitution and income effects using Slutsky equation. But after I derive the Hicksian demand functions for e.g. x:

$$h\_x= \frac{I}{p\_x+\frac{p\_y^3}{p\_x^2}}$$

do we derive this only with respect to x in order to account for impacts of changes in $p\_x$ or do I do the same derivation with respect to y and sum both up?

The confusing part is that I don't know what prices change, so it would seem most generally to assume that both change.