Final answer:
Two words that would never sensibly describe any linear system could be 'inconsistent' and 'dependent' as the former implies no solution exists while the latter requires a solution that expresses a relationship between variables.
Step-by-step explanation:
The question asks us to write two words that would never sensibly describe any linear system. In the context of linear systems, the terms consistent and inconsistent are used to describe whether a system of equations has solutions (consistent) or not (inconsistent). Meanwhile, dependent and independent usually refer to whether one variable can be determined from another (dependent) or can vary freely (independent).
In terms of a nonsensical combination that would never apply to any linear systems, we could pair 'consistent' (which suggests a coherent solution exists) with 'independent' (suggesting each equation in the system can vary without affecting others). However, this pairing does not outright violate any mathematical concepts when taken individually. On the other hand, 'inconsistent dependent' could imply a more clearly nonsense description of a system as a dependent system, by definition, has relationships between its variables, whereas an inconsistent system suggests the absence of a solution, preventing any dependent relationship.