Suppose we have two quanitities X and Y and we try to find out if a third quantity Z depends on them.
1st case Changing the X holding Y constant doesn't change Z.
2nd case Changing the Y holding X constant changes Z.
3nd case Changing both X and Y (simultaneously) changes Z.
Can from the first two cases conclude that Z does not depend on X? What if we change both X and Y simultaneously and now Z changes differently than the 2nd change? For example if Y were doubled in the 2nd case then Z doubled but in the 3rd case doubling Y quadrupled Z (no matter what change X undergoes). Could we say in that case that Z does not depend on X?