A supply system of a sealing system of a turbomachine, wherein the sealing system which are suppliable with a seal gas. The supply system comprises, for each sealing sub-system, four seal gas lines: a first seal gas supply line, via which process gas extracted from the turbomachine is suppliable as first seal gas to the respective sealing sub-system. A second seal gas supply line, via which second seal gas is suppliable to the respective sealing sub-system. A seal gas discharge line, via which the first seal gas and the second seal gas are dischargeable from the respective sealing sub-systems. A safety discharge line, which is closed during the normal operation and open in the event of a fault, to discharge at least one part of the first seal gas and of the second seal gas from the respective sealing sub-system via the same in the event of a fault.