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In this article, we study an energy-efficient nonorthogonal multiple access (NOMA) enabled multiaccess edge computing (MEC) system with strict latency requirements. We aim to minimize the energy consumption of all users by optimizing the resource allocation (including power and computation resources) and subchannel assignment, subject to the given latency constraint. The formulated problem, however, is a nonconvex combinatorial optimization problem. Nevertheless, we decompose the problem into a resource allocation subproblem and a subchannel assignment subproblem, and then solve the two subproblems iteratively. On one hand, we investigate the hidden convexity of the resource allocation subproblem under the optimal conditions, and propose an efficient algorithm to optimally allocate the resources by dual decomposition methods. On the other hand, we formulate the subchannel assignment subproblem into an integer linear programming problem and strictly prove that the problem is nondeterministic polynomial-time hard. We then solve it optimally by branch-and-bound methods, which is shown to be efficient in extensive simulations. Moreover, through considerable simulation results, we show that our proposed algorithm helps greatly reduce users' energy consumption when communication resources (e.g., bandwidth) are limited. Additionally, it is verified that NOMA outperforms orthogonal multiple access in multiuser latency-sensitive MEC systems.