Inconsistent equation

Definition

An inconsistent equation is a linear equation with no solution. It represents lines that are parallel and never intersect.

5 Must Know Facts For Your Next Test

1. An inconsistent equation results in a false statement, such as $0 = 1$ when simplified.
2. Graphically, inconsistent equations represent parallel lines that do not meet.
3. Inconsistent systems have no points in common; their solution set is empty.
4. In a matrix form, an inconsistent system will show at least one row where all coefficients are zero but the constant term is non-zero.
5. Inconsistent equations contrast with consistent equations which have at least one solution.

Review Questions

• What does it mean for an equation to be inconsistent?
• How can you identify an inconsistent equation from its simplified form?
• What does the graph of an inconsistent system look like?

Related terms

Consistent Equation: A linear equation or system of equations that has at least one solution.

Dependent Equation: A linear equation or system of equations where all the equations describe the same line, resulting in infinitely many solutions.

Augmented Matrix: A matrix that includes the coefficients and constants of a system of linear equations, used to solve the system.