A brake system includes two brake circuits having brake circuit lines for two vehicle axles and at least one hydraulic wheel brake in each brake circuit. Each wheel brake is connectable to a corresponding brake circuit or brake circuit line via a paired switch valve for pressure build-up and release in the wheel brake using a pressure supply device that can build up pressure in both brake circuits. At least one circuit separating valve blocks or releases a hydraulic connection line connecting the two brake circuits. At least one outlet valve connects an accumulator container to at least one brake circuit to release pressure. A master cylinder having only one working chamber is actuable by a brake pedal. The working chamber is connectable to the brake circuit line of a brake circuit. A switch valve is used to close or release the hydraulic line.