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In this paper, we study the power allocation and relay selection strategy for two-way relaying systems using physical-layer network coding (PNC), in which two information symbols can be exchanged in two time slots. Our approach is based on maximizing the objective rate under a total power budget consumed by the transmission of the two information symbols. Two optimization objectives, namely, the minimum of the achievable rates of the two directions and the sum rate of the system, are considered here. Since the objectives are not continuously differentiable functions, we propose a method based on a suboptimal solution to solve the original problems. It is shown that the main problems have closed-form solutions, and the strategies can be implemented in a distributed manner. The numerical results verify the effectiveness of our proposal.