How did Chief Justice Marshall resolve each of the two issues in McCulloch v. Maryland?

Chief Justice Marshall resolved both of the issues in this case in favor of the federal government.

With respect to the issue of constitutionality, Marshall appealed to the “elastic clause” in the Constitution.  That clause said that Congress could do anything that was “necessary and proper” for carrying out the powers that are explicitly given to it in the Constitution.  Therefore, the Constitution implied that Congress could create a bank.

With respect to the issue of federalism, Marshall upheld national supremacy.  He said that a state could essentially destroy a part of the federal government (like the bank) by taxing it.  This would allow states to be supreme over the federal government.  Therefore, states could not tax activities of the federal government.