Networked systems are useful for a wide range of applications, many of which require distributed and collaborative data processing to satisfy real-time requirements. On the one hand, networked systems are usually resource constrained, mainly regarding the energy supply of the nodes and their computation and communication abilities. On the other hand, many realtime applications can be executed in an imprecise way, where an approximate result is acceptable as long as the baseline Quality-of-Service (QoS) is satisfied. Such applications can be modeled through Imprecise Computation (IC) tasks. To achieve a better trade-off between QoS and limited system resources, while meeting application requirements, the IC-tasks must be efficiently mapped to the system nodes. To tackle this problem, we firstly construct an IC-tasks mapping problem that aims to maximize system QoS subject to real-time and energy constraints. Dynamic Voltage and Frequency Scaling (DVFS) and multi-path routing are explored to further enhance real-time performance and reduce energy consumption. Secondly, based on the problem structure, we propose an optimal approach to perform IC-tasks mapping and prove its optimality. Furthermore, to enhance the scalability of the proposed approach, we present a heuristic IC-tasks mapping method with low computation time. Finally, the simulation results demonstrate the effectiveness of the proposed methods in terms of the solution quality and the computation time.