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If the partial pressure of one of the reactants increases, then the reaction will shift right and produce more products, increasing the products' partial pressures. The partial pressure of the other reactants therefore decreases.
I'm not sure how it would be possible to increase the pressure of one type of gas in the same reaction vessel as the other. However, assuming that this change in pressure essentially causes a change in concentration, the other reactant would only be affected as a result of LeChatellier's principle. The increase in concentration of the reactants would cause an imbalance in the equilibrium "seesaw" (or more mathematically Q<K now) and the reaction will run forward more. This would result in the consumption of the second reactant to produce more product, ultimately decreasing its concentration.
If the partial pressure of one reactant increases, then the partial pressure of the other reactant will decrease (as long as this pressure increase comes from a decrease in volume). Since increasing the pressure causes the concentration of the reactant to increase, the equilibrium will shift to the right so as to increase the concentrations and thus the partial pressures of the products.
In a chemical reaction, if one reactant is increased in pressure, the other will decrease to try and balance it, but ultimately the concentration then becomes higher and the equilibrium shifts to the products where pressure increases.
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