An inconsistent system is a set of equations that has no solution. This typically occurs when the equations represent parallel lines that never intersect.
5 Must Know Facts For Your Next Test
Inconsistent systems have no points of intersection, meaning they have no common solution.
Graphically, inconsistent systems are represented by parallel lines in two-variable cases.
For three-variable systems, inconsistency can occur if the planes do not intersect at a common point or line.
Algebraically, an inconsistent system results in a contradiction such as $0 = 1$ when solving the equations.
The determinant of the coefficient matrix in an inconsistent system is zero, but this alone does not confirm inconsistency without further evaluation.