The "Ostwald Isolation Method": How does this work?
The powers $x$ and $y$ are intrinsic to the reaction (at least if the reaction pathway remains the same) and will not vary with reaction parameters, so that adding them then poses no difficulty. 

More specifically, it is presumed that the reaction rate is given by an equation of the form $$r = c\ce{[A]}^x\ce{[B]}^y;$$ the Ostwald isolation method finds the powers $x$ and $y$ by flooding the system with $\ce{B}$ and $\ce{A}$ respectively in excess in two separate experiments, so that in the former case we have $$r = (c\ce{[B]}^y)\ce{[A]}^x \approx k\ce{[A]}^x$$ and in the latter $$r = (c\ce{[A]}^x)\ce{[B]}^y \approx j\ce{[B]}^y.$$

Adding the powers $x$ and $y$ gives the order of reaction by definition.



Incidentally, Wikipedia lists this method as the 'method of flooding', here.