This study deals with the in-plane motion of a free-floating planar satellite equipped with two thrusters whose force directions are fixed with respect to the satellite. The system's governing equations form non-integrable second-order "nonholonomic" constraints due to the fixed force directions within the satellite. First, this paper shows the general expressions of the system's equations of motion, and shows that its translational and rotational motions can not be controlled independently. Next, by assuming an imaginary thruster controlled by a feedback law, we transform the nonholonomic constraints into holonomic ones. This concept is followed by a strategy to achieve a rotational motion without drift for a satellite system with two fixed thrusters. Afterwards, this paper shows a procedure for precise control of the position and attitude of the system. The validity of the proposed method is verified by numerical simulations. Finally, this paper discusses the special case when the magnitude of the thruster force is taken constant.