Final answer:
In order to add a function to a system without changing the solution set, the new function should be consistent with the current system of equations.
Step-by-step explanation:
In order to answer this question, we need to understand what it means to add a function to a system. Adding a function to a system refers to incorporating a new mathematical expression into the existing equations that model the system. The solution set of a system of equations represents the values that satisfy all the equations within the system. If we want to add a function to the system without changing the solution set, it means that the new function should not introduce any additional solutions or change the existing solutions. In other words, the new function should be consistent with the current system of equations. For example, if we have a system of two linear equations, adding a linear function that is proportional to one of the existing equations does not change the solution set. However, adding a quadratic function or an exponential function would introduce new solutions and change the solution set.