What fundamental law is demonstrated in balancing equations?
The law of conservation of mass, or mass balance.
If you start with 10 g of reactant (from all sources), AT MOST you are going to get 10 g of product; in fact you are not are even going to get that because your ability to scrape product from the reaction vessel is not perfect.
MASS IS CONSERVED IN EVERY CHEMICAL REACTION!
Is mass conserved in every nuclear reaction?