A given systems of equations is said to be inconsistent if

The correct option is "it has no solutions".

In algebra, a system of equations is a collection of two or more equations sharing a common set of variables. When we analyze a system of equations, we classify it based on the number of solutions it possesses. Specifically, systems are categorized into two main types:
1. Consistent System: A system of equations that has at least one solution. This category includes systems with exactly one unique solution (where the lines or planes intersect at a single point) and systems with infinitely many solutions (where the equations represent the same line or plane, meaning they coincide).
2. Inconsistent System: A system of equations that has no solutions whatsoever. This occurs when there is no set of values for the variables that can satisfy all the equations simultaneously. For example, in a two-dimensional space, a system representing two parallel but distinct lines is inconsistent because the lines never intersect.

Therefore, by mathematical definition, a given system of equations is said to be inconsistent if it has no solutions.