A turboexpander and driven turbomachine system comprising a turboexpander configured for expanding a first fluid and comprising an expander stage with one expander impeller; a first set of moveable inlet guide vanes at the inlet of the expander stage; a driven turbomachine configured for processing a second fluid and comprising a turbomachine impeller; a second set of moveable inlet guide vanes at the inlet of the turbomachine impeller; a mechanical transmission between the turboexpander and the driven turbomachine; and a controller connected to the second set of moveable inlet guide vanes and configured for controlling the second set of moveable inlet guide vanes for adjusting the rotary speed of the driven turbomachine and said turboexpander.