An electrolyzing system for electrolyzing a brine solution of water and ions of an alkali salt to produce acidic electrolyzed water and alkaline electrolyzed water, the system comprising: a vessel for containing the brine solution comprising cations and anions and defining a brine bath; an electrolytic cartridge arranged in said vessel and immersed in the brine bath; a direct current power supply; said electrolytic cartridge comprising a cathode cell and an anode cell; characterized by: said cathode cell including a pair of cathode electrodes (C1, C2) connected to the direct current electrical supply that negatively charges the cathode electrodes; a cathode electrode holder supporting said cathode electrodes in coplanar laterally spaced side by side relation to each other in respective chambers sealed from each other; a cation permeable membrane disposed on one side of each of said cathode electrodes defining a space between each cathode electrode and the cation permeable membrane through which cations from the brine solution can enter through the cation permeable membrane; said spaces between cathode electrodes and cation permeable membrane each being in communication with a fresh water supply inlet at an inlet end of the space and in communication with a cleaning chemical outlet at an outlet end of the space; said spaces between said cathode electrodes and cation permeable membrane being sealed off from each other and the brine solution such that the only path for the brine solution to enter the spaces is through the cation permeable membrane; said anode cell including a pair of anode electrodes (A1, A2) connected to the direct current electrical supply that positively charges the anode electrodes; an anode electrode holder supporting said anode electrodes in coplanar laterally spaced side by side relation to each other in respective chambers sealed from each other; an anion permeable membrane disposed on one side of said anode electrodes defining a space between each anode electrodes and the anion permeable membrane through which anions from the brine solution can enter through the anion permeable membrane; said spaces between said anode electrodes and anion permeable membrane each being in communication with a fresh water supply inlet at an inlet end of the space and in communication with a cleaning chemical outlet at an outlet end of the space; and said spaces between said anode electrodes and anion permeable membrane being sealed off from each other and the brine solution such that the only path for the brine solution to enter the spaces is through the anion permeable membrane. a vessel for containing the brine solution comprising cations and anions and defining a brine bath; an electrolytic cartridge arranged in said vessel and immersed in the brine bath; a direct current power supply; said electrolytic cartridge comprising a cathode cell and an anode cell; said cathode cell including a pair of cathode electrodes (C1, C2) connected to the direct current electrical supply that negatively charges the cathode electrodes; a cathode electrode holder supporting said cathode electrodes in coplanar laterally spaced side by side relation to each other in respective chambers sealed from each other; a cation permeable membrane disposed on one side of each of said cathode electrodes defining a space between each cathode electrode and the cation permeable membrane through which cations from the brine solution can enter through the cation permeable membrane; said spaces between cathode electrodes and cation permeable membrane each being in communication with a fresh water supply inlet at an inlet end of the space and in communication with a cleaning chemical outlet at an outlet end of the space; said spaces between said cathode electrodes and cation permeable membrane being sealed off from each other and the brine solution such that the only path for the brine solution to enter the spaces is through the cation permeable membrane; said anode cell including a pair of anode electrodes (A1, A2) connected to the direct current electrical supply that positively charges the anode electrodes; an anode electrode holder supporting said anode electrodes in coplanar laterally spaced side by side relation to each other in respective chambers sealed from each other; an anion permeable membrane disposed on one side of said anode electrodes defining a space between each anode electrodes and the anion permeable membrane through which anions from the brine solution can enter through the anion permeable membrane; said spaces between said anode electrodes and anion permeable membrane each being in communication with a fresh water supply inlet at an inlet end of the space and in communication with a cleaning chemical outlet at an outlet end of the space; and said spaces between said anode electrodes and anion permeable membrane being sealed off from each other and the brine solution such that the only path for the brine solution to enter the spaces is through the anion permeable membrane.