When the constitution was created, it was created to solve problems that appeared after the enactment of the Articles of Confederation such as the inability to gather funds from the states as well as the division it created. This is how the federal system we have today came to be and one of the main reasons it divides the power between the Federal and State governments. This federalist design created decades ago has worked well at striking the balance that the Articles of Confederation were not able to. The two key things specifically that allowed the success of this federalist design was the Tenth Amendment and the creation of the Supreme Court.
The Tenth Amendment states that any power not specifically given to the federal government is reserved to the states. This amendment specifically is key to the success of the federal system due to how it provides power to the states but at the same time reserves some to the federal government and restricts the federal government. One of the biggest worries about this type of government that appeared during its ratification process through Brutus 1, a paper published against the Constitution's ratification was how the government would one day be above the people's power causing people to become as powerless as they were under the monarchy of Britain. This Tenth Amendment prevents this power creep from occurring by restricting the federal government to the abilities stated in the constitution. An example of this is if a state decided to allow homeowners to kill trespassers on their property, this particular example is a law many states have in the US. Even if it may seem harsh and unethical the federal government can not do anything about this as the power granted upon them in the Constitution says nothing about being able to change a state's law, however, they have the power to review such a law if it becomes troublesome. This reservation of powers, however, goes even further in more amendments such as protecting citizens' rights and forcing states to acknowledge the Bill of Rights under the 14th amendment. The states can create their own laws and still hold on to their freedom but the leash on them is still there, creating a successful balance between the federal and state governments.
The creation of the Supreme Court may seem an odd thing to say contributed to the success of this federal system, but it is the most important point of the two. The Supreme Court is a court for the most controversial holdings made, unlike other courts however the end game of every preceding is to decide if a holding in a case was constitutional or not. This power came about after the case of Marbury v Madison allowing the Supreme Court to decide if something is constitutional or not and if not strike it down immediately. This power allows the federal government to overcome the restriction caused by the Tenth Amendment and creates a balance of power between the Federal and State fairly. Take Brown v Board of Education, for example, this specific case was used to declare "separate but equal" unconstitutional and end it as it was impossible to stop states from doing it any other way. Another example would also be Gideon v Wainwright or most any supreme court case, the biggest commonality of them all is each of them influenced a state law or what a state enacted in a fair manner.
In the end, this balance created by the Supreme Courts' power of Judicial Review and the Tenth Amendment is what makes the relationship between federal and state governments work so well. Without the Tenth Amendments, state governments would be powerless and it would affirm the worries expressed in Brutus 1. Without the power of judicial review, the states would become uncontrollable and it would become the Articles of Confederation all over again. This division of powers has ensured the balance between the needs of society on a larger scale and the interests of citizens at a local level that we experience today and will continue to do so in the foreseeable future. I could not think of a better system to create the delicate balance the federalist design has.
