A brake system includes a brake pedal for actuating a master cylinder having two pistons and corresponding pressure chambers, where the system can be operated in a brake-by-wire mode and also a fallback mode. The system also includes a first electrically controllable pressure source and a second electrically controllable pressure source. The first and second electrically controllable pressure sources each have corresponding output flows that are connected together. The second electrically controllable pressure source can therefore provide output volume flow in the event the first electrically controllable pressure source fails.