Explain how a federal system of government delegates powers between state and national government?

Under the Tenth Amendment, the powers that are not expressly given to the federal government are reserved to the states or the people. The enumerated powers in the constitution (and their related implied powers) are powers the federal government has. The state governments retain all of the other powers. Some powers are concurrent; the federal government has been given the power, but it hasn't been prohibited to the states, so they also can exercise it. An example would be the ability to tax.