Consistent Equations

a system of equations such that there exists a set of values of the variables that satisfies each equation. For example, the equations x² + y² = 13 and x + y = 5 are consistent, since they are satisfied by the values x = 2 and y = 3. The equations x² + y² = 13 and 2x² + 2y² = 5, on the other hand, are inconsistent. Geometrically, the consistency of a system of equations means that the sets of points representing the equations share a common point.