Final answer:
The mathematical technique that underlies the reciprocal cost allocation method is Simultaneous equations.
Step-by-step explanation:
The mathematical technique that underlies the reciprocal cost allocation method is Simultaneous equations. In the reciprocal cost allocation method, the cost of a service department is allocated to other departments based on the reciprocal of the services received. This allocation method can be represented by a system of simultaneous equations, where each equation represents the allocation of costs from one department to another.