The core purposes of the system of checks and balances is to

The core purposes of the system of checks and balances is to: Prevent any one person or branch from becoming too powerful. To make legally null and void; to invalidate.

your answer is

to dominate europe

and i know for a fact it can't be the others

although the crusades failed to capture jerusalem, they had several major impacts on western europe. they increased the authority of the king: sometimes nobles died in battle without leaving an heir in which case the king got their land. kings passed taxes to pay for the crusades.