A system supplies a fluid to an evaporator of a refrigeration unit and has first and second lines connected to a fluid inlet of the evaporator. The system has an expansion valve with a continuously modifiable first flow cross section, disposed in the first line, the continuously modifiable first flow cross section setting a first mass flow through the first line. A shut-off device is disposed in the second line and switchable discretely between an open position and a closed position. A throttle with a constant second flow cross section is disposed in the second line. A control unit continuously modifies the first flow cross section of the expansion valve and controls the shut-off device as a function of the first flow cross section.