1. The problem involves understanding when to apply a certain method to a system of equations or conditions. 2. A system is called consistent if it has at least one solution. 3. A system is non-trivial if it is not the trivial case (e.g., not all zero or not all identical equations). 4. The method mentioned is applied when the system is both consistent and non-trivial, meaning it has meaningful solutions to find. 5. This ensures that the method will yield useful results rather than trivial or no solutions. 6. In summary, always check for consistency (existence of solutions) and non-triviality (meaningful, non-zero solutions) before applying the method.