Inconsistent equation

Definition

An inconsistent equation is a linear equation in one variable that has no solution. This occurs when the equation simplifies to a contradiction, such as $0 = 1$.

5 Must Know Facts For Your Next Test

1. An inconsistent equation results when the variables cancel out and a false statement remains.
2. $ax + b = c$ is an inconsistent equation if $a = 0$ and $b \neq c$.
3. Graphically, an inconsistent equation represents parallel lines that never intersect.
4. Inconsistent systems have no points of intersection because they have different constant terms but are otherwise identical.
5. Identifying inconsistency involves simplifying the equation until you see if it leads to a contradiction.

Review Questions

• What does it mean for an equation to be inconsistent?
• How can you identify an inconsistent equation through simplification?
• What is the graphical representation of an inconsistent system of equations?

Related terms

Consistent Equation: A consistent equation has at least one solution. In linear systems, this means at least one point where the graphs intersect.

Contradiction: A logical statement that is always false, such as $0 = 1$. It indicates that an equation or system of equations has no solution.

$a\ne b$: $a \ne b$ signifies two values are not equal. In the context of equations, it's often used to show inconsistency.