# Simultaneous Equation Method
Another reciprocal-service method. Instead of iterating, we set up algebraic equations to find the grossed-up (final) cost of each service department, then apportion that final cost to production departments.
## Procedure
1. Let x = final total cost of Service Dept-1 and y = final total cost of Service Dept-2 (after receiving share from the other).
2. Write two simultaneous equations:
- x = (primary cost of S₁) + (share received from S₂)
- y = (primary cost of S₂) + (share received from S₁)
3. Solve the equations to find x and y.
4. Apportion x and y to production departments in the given ratio.
## When to Prefer This Method
- Exam questions with only 2 service departments with reciprocal service — fastest and cleanest.
- Eliminates iteration arithmetic errors of the Repeated Distribution method.