What is a consistent system in equations?

A consistent system in equations refers to a situation where the equations in the system are able to find at least one set of values for the variables that satisfies all the equations simultaneously. This definition highlights the key feature of consistency: the existence of solutions.

When a system has at least one solution, it means the lines or planes represented by the equations intersect at least at one point, thereby fulfilling the requirement of consistency. This can manifest in different forms; there may be exactly one solution where the equations intersect at a single point, or there may be infinitely many solutions if the equations represent the same line or plane. The critical aspect is that there is no scenario where the lines are parallel or non-intersecting, ensuring that at least one solution is present.

In contrast, a system that has no solutions is termed inconsistent, and that would not qualify as consistent. Therefore, the definition of a consistent system accurately leads to the understanding that it encompasses all cases where solutions exist, making the correct option one that includes any scenario with at least one solution.