A system having a cover for a motor vehicle, in particular a fuel cap or a charging port cover, an electromotive actuator with an output and an electric motor, and an electric motor controller, wherein the electric motor of the actuator can be controlled via the motor controller as a function of an electric actuation signal such that the output of the actuator transfers the cover to an open position or a closed position. In order to realize the automatic opening or closing of a cover for a motor vehicle using simple circuit technology, it is proposed that the actuation signal can be generated by an external movement of the output. Furthermore, a method for automatically actuating a cover is provided.