Systems of Equations: Consistent, Inconsistent, Dependent, Independent
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More Lessons for Grade 11 Algebra
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Examples, solutions, videos, worksheets, games, and activities to help Algebra students learn how to apply systems of linear equations.
Systems of Equations
A system of equations is a set of two or more equations with the same set of variables. Systems are classified based on whether they have solutions (consistent) or no solution (inconsistent).
The following diagrams show consistent and inconsistent systems. Scroll down the page for more examples and solutions of consistent and inconsistent systems.
Algebra Worksheets
Practice your skills with the following worksheets:
Printable & Online Algebra Worksheets
1. Consistent System
Definition: A system with at least one solution.
Types:
Independent: Exactly one unique solution (lines intersect at one point).
Dependent: Infinitely many solutions (lines are identical).
How to Identify
Graphically:
Independent: Lines intersect at one point.
Dependent: Lines overlap completely.
Algebraically:
Solve the system.
Independent: Get One solution.
Dependent: A true statement (e.g., 0 = 0).
2. Inconsistent Systems
Definition: A system with no solution (lines are parallel and never intersect).
How to Identify
Graphically: Lines are parallel and distinct.
Algebraically: Solving leads to a false statement (e.g., 0 = 5).
Videos
Consistent and Inconsistent Systems
Consistent and Inconsistent
Independent and Dependent Systems
Substitution (Dependent & Inconsistent)
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