 # Solving Systems of Equations and Inequalities

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A series of free Basic Algebra Lessons.

In this lesson, we will learn

• inconsistent and dependent systems of equations
• how to solve systems of equations using matrices
• how to solve systems of inequalities by graphing
Inconsistent and Dependent Systems of Equations
A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel. A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions. These two situations occur when trying to solve for a system of equations.

Consistent and independent systems, consistent and dependent systems, and inconsistent systems

Solving Systems using Matrices
A system of equations is two or more equations that contain the same variables. Solving systems using matrices is one method to find the point that is a solution to both (or all) original equations. Besides solving equations using matrices, other methods of finding the solution to systems of equations include graphing, substitution and elimination.

Solving a System of Linear Equations Using Inverses of Matrices
Solve a 2 x 2 system using inverses (find using determinants).
Using the inverse of a matrix to solve a system of equations Systems of Inequalities
When solving systems of inequalities, you are solving for a solution region. A solution region is the collection of points that are solutions to both inequalities. Solving systems of inequalities combines knowledge of graphing lines, graphing inequalities and solving systems of equations.

Graphing Systems of Linear Inequalities

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  