No, the stock system is not used for balancing chemical reactions. The stock system is a naming convention for chemical compounds that contain metal ions with multiple oxidation states. It is used to distinguish between different compounds of the same metal, such as iron(II) chloride (FeCl2) and iron(III) chloride (FeCl3).
To balance a chemical reaction, you need to know the number of atoms of each element on both sides of the reaction equation. Once you have this information, you can adjust the coefficients of the reactants and products so that the number of atoms of each element is the same on both sides of the equation.