The Olive Branch Petition was their last attempt to keep peace with Britain. They ticked the king off, and now after the battle of Lexington and Concord, the king is getting scary and they want his forgiveness. The OBT was sent to tell the king that the colonists would be loyal again.
Answer: The best example of checks and balances is that the president can veto any bill passed by Congress, but a two-thirds vote in Congress can override the veto.