What type of system of equations has exactly one solution?

A system of equations that has exactly one solution is categorized as an independent system. Independent systems consist of lines that intersect at a single point, which represents the solution to the equations involved. This means that there is a unique set of values for the variables that satisfy all equations in the system simultaneously.

In contrast, a dependent system has an infinite number of solutions, where the equations essentially represent the same line, leading to overlapping solutions. An inconsistent system, on the other hand, has no solution at all because the lines are parallel and do not intersect. While the term "linear system" is applicable here, it is a broader category that includes all types of systems formed by linear equations, including dependent and inconsistent systems. Thus, the term "independent system" is the most specific and accurate descriptor for a system with exactly one solution.