Balanced equations illustrate what law? the law of conservation of mass the law of proportional elements the law of coefficients the law of balanced atoms

Answer is: the law of conservation of mass.

Number of atoms must be the same on left and right side of balanced chemical reaction according to the law of conservation of mass or principle of mass conservation.
For example balanced chemical reaction:
BaCl₂ + H₂SO₄ → BaSO₄ + 2HCl.
There are two hydrogen atoms, one sulfur atom, four oxygen atoms, one barium atom and two chlorine atoms on both side of this chemical reaction.