For carbonating a precursor liquid (2), such as water, to form a beverage, a carbon dioxide source in solid form (41) having adsorbed carbon dioxide is provided in a cartridge (4) which is used to generate carbon dioxide gas that is dissolved into the precursor liquid (2). A beverage medium (42), such as a powdered drink mix or liquid syrup, may be provided in the same or a separate cartridge (4) as the carbon dioxide source (41) and mixed with the precursor liquid (2) to form a beverage. The use of one or more cartridges (4) for the carbon dioxide source and/or beverage medium may make for an easy to use and mess-free system for making carbonated beverages, e.g., in the consumers home, by means of a beverage forming machine (1).