Intermediate Algebra Systems Linear Equations

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Intermediate Algebra

4. Systems of Linear Equations and Inequalities

Description

After exploring one linear equation in two variables, we explore the aspects of more linear equations in two variables called a system of equations. We explore how to solve a system of equations using the Graphing, Substitution, and Elimination Methods. Extending our concepts from Elementary Algebra, we explore how to solve systems of linear equations in three or more variables; solving a system of equation using determinants and Cramer's Rule; and solving systems of linear equations using matrices. We explore graphing linear inequalities in two variables; linear programming and finish with applying these skills to real world situations.

Sections in this topic include:

1. Solving Systems of Linear Equations by Graphing, Elimination and Substitution

Refreshing our knowledge from Elementary Algebra, we explore how to solve a system of equations using the graphing, elimination and substituion methods. Groups within this section include: solving systems by graphing; solving systems by using the elimination method; solving systems by using the substitution method; solving systems containing rational expressions; determining a system that passes through a pair of points.

2. Solving Systems of Linear Equations in Three or More Variables

Expanding our knowledge, we investigate how to solve systems of linear equations in three or more variables. The group contained within this section is: solving systems of linear equations in three or more variables.

3. Determinants and Cramer's Rule

In 1750, Gabriel Cramer invented a way to solving a system of linear equations using determinants. Today, we apply his discovery to solving systems of linear equations. Groups within this section include: evaluating determinants; solving a determinant equation; using Cramer's Rule to solve a system of equations using determinants.

4. Solving Systems of Linear Equations Using Matrices

This section addresses the last way of solving a system of equations using matrices and row operations.

5. Graphing Linear Inequalities in Two Variables

Expanding our knowledge of how to solve a system of equalities, we next explore how to solve a system of inequalities by graphing half-planes and determining regions where the half planes intersect (and therefore are the solutions of the system of linear inequalities in two variables). Groups included in this section contain: Solving an inequality by graphing; solving a system of inequalities by graphing.

6. Linear Programming

One application of graphing linear inequalities in two variables is to use the method of linear programming to solve complex real world scenarios.

7. More Applications

In this section, we investigate applying our skills of solving system of equations to solve real world scenarios.

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