An electrolyzing system for electrolyzing a brine solution of water and an alkali salt to produce acidic electrolyzed water and alkaline electrolyzed water is provided. The system includes an internal chamber for receiving the brine solution and two electrolyzer cells immersed in a brine bath. Each electrolyzer cell includes an electrode, at least one ion permeable membrane supported relative to the electrode to define a space communicating between a fresh water supply and a chemical outlet into which brine enters only through the membrane. One of the electrodes is coupled to a positive charging electrical supply and the other to a negative charging electrical supply.