Final answer:
The Reciprocal method is used to account for all reciprocal flows between service departments using simultaneous equations.
Step-by-step explanation:
The method that considers all reciprocal flows between service departments through simultaneous equations is the Reciprocal method. This method recognizes the reality that service departments often provide services to each other and not just to the producing departments. To account for these interdependencies, the Reciprocal method uses a system of simultaneous equations to allocate service department costs, ensuring an accurate and comprehensive distribution of overhead costs.