1. The problem is to understand the concept of consistency in a mathematical or logical context. 2. Consistency means that a set of statements or equations does not contain any contradictions. 3. For example, in algebra, a system of equations is consistent if there is at least one solution that satisfies all equations simultaneously. 4. To check consistency, one can use substitution, elimination, or matrix methods like row reduction. 5. If no contradictions arise and solutions exist, the system is consistent; otherwise, it is inconsistent. 6. Understanding consistency is crucial for solving equations and verifying logical arguments.