Explain the constitutional basis of the system of checks and balances. Why is this principle is important? Provide examples of a major check possessed by each branch government.

The system of checks and balances in the United States government exists to make sure no one branch is too powerful. It prevents a single branch from controlling the government and the country. Checks and balances limit each branch's individual power by making sure that all the branches have to work together to pass laws and govern.
The executive branch has a veto power and can make foreign treaties. It also appoints federal judges. The president cannot fire Supreme Court judges. They can veto laws that Congress wants to pass. 
The legislative branch can override a presidential veto to pass a law. They also approve presidential appointments and treaties. They investigate suspicious actions by the executive branch and hold the powers of impeachment.
Judicial review is a power belonging to the judicial branch. It allows a court to declare a law invalid if they feel it conflicts with the constitution. This is a check on the legislative branch and on the executive branch since they can also rule that a presidential law or action is unconstitutional. 
Meanwhile, the president appoints federal judges and the legislative branch must approve them.
https://www.lsusd.net/cms/lib6/CA01001390/Centricity/Domain/230/Learning_Center_9.pdf