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:
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.