Consistent and inconsistent are terms used in mathematics to describe systems of equations. A system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system, making each equation hold true as an identity. In contrast, a system of equations is called inconsistent if there is no set of values for the unknowns that satisfies all of the equations. If a system of equations is inconsistent, then it is possible to manipulate and combine the equations in such a way as to obtain contradictory information, such as 2 = 1.
A system of linear equations can have one solution, an infinite number of solutions, or no solution. If a system has at least one solution, it is said to be consistent. If a consistent system has exactly one solution, it is independent. If a consistent system has an infinite number of solutions, it is dependent. When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent. The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
In summary, consistent and inconsistent are terms used to describe systems of equations in mathematics. A system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system, while a system of equations is called inconsistent if there is no set of values for the unknowns that satisfies all of the equations.
