I guess this depends upon what you mean by the solution of chemical equations. Chemistry follows good rules and every atom needs to be accounted for. I guess then that there are patterns – nice and orderly!
e.g. C6H12O6+ 6O2—> 6CO2+ 6H2O for glucose metabolism
Yes – you must have the same atoms on the left and right although they are in different combinations. In chemical reactions atoms do not disappear they just get arranged differently into different molecules and compounds
Chemical equations must always balance. There must be the same amount of the different elements on both sides of the equation, as no chemical reaction actually changes any of the elements. (There are nuclear reactions in which this does happen, like, for example, the radioactive decay of uranium-238 to thorium-234).