Inconsistent System
An inconsistent system of linear equations is a pair of equations that has no common solution. Geometrically, this occurs when the two equations represent parallel lines on a graph that never intersect.
Key Concepts
An inconsistent system yields no solution because there is no single point (x, y) that satisfies both equations simultaneously.
When graphed, the lines of an inconsistent system are strictly parallel and maintain a constant distance from each other.
Algebraically, a pair of linear equations is inconsistent if the ratio of the coefficients of x is equal to the ratio of the coefficients of y, but not equal to the ratio of the constant terms.
Real World Applications
Two parallel railway tracks that run alongside each other but never cross or meet at any point.
The opposite edges of a rectangular ruler or a straight road where the two sides never intersect.