# Ch 19: NES Math: Systems of Equations

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### About This Chapter

## NES Math: Systems of Equations - Chapter Summary

Use this chapter's lessons to review information on solving various types of linear and non-linear equations. Our videos will help you brush up on topics for the NES Math test including:

- Solving systems of linear or nonlinear equations in two variables
- Solving a system of linear equations in three variables, either with a solution or with no or infinite solutions
- Writing an augmented matrix for a linear system
- Solving systems of linear equations in two or three variables using determinants

Our instructors understand what success on the NES Math test requires, and they use plenty of examples and practice problems, along with a good dose of humor, to get their points across in these enjoyable lessons. You can even contact them through our ask-an-expert message board if you have questions. Lesson quizzes help you assess your learning, and you can track your study progress through our Dashboard.

### NES Math: Systems of Equations Chapter Objectives

Passing the NES Math exam is one of the requirements for certification to teach secondary-level math in five states. The test consists of multiple-choice questions that require you to work a problem or read a question and choose the best response from several options. Our quizzes give you practice answering questions in this format.

The questions on the NES Math test are divided into five content domains, and questions on Systems of Equations are in the Patterns, Algebra and Functions content domain. This is the largest content domain and accounts for 24% of the total score.

### 1. How to Solve a System of Linear Equations in Two Variables

Watch this video lesson to learn how you can solve a system of linear equations in two variables by using the substitution method. Learn how easy it is to use on any linear system in two variables.

### 2. How to Solve a Linear System in Three Variables With a Solution

After watching this video lesson, you will be able to solve a linear system in three variables using the elimination method. Learn the simple operations that are needed to solve your system.

### 3. How to Solve a Linear System in Three Variables With No or Infinite Solutions

In this video lesson, you will learn to recognize when a linear system has no solution or an infinite number of solutions. You will also learn how to go about solving each of these types of systems.

### 4. How to Write an Augmented Matrix for a Linear System

Watch this video lesson to learn how you can turn your system of equations into matrix form. The matrix form is another way of writing your linear system that is sometimes easier to work with.

### 5. Solving Systems of Linear Equations in Two Variables Using Determinants

Watch this video lesson to learn how you can easily find the solution of a linear system in two variables by just using determinants. All you need to find the complete solution is to find three determinants.

### 6. Solving Systems of Linear Equations in Three Variables Using Determinants

Watch this video lesson to learn how to use Cramer's rule to help you find your solutions by finding just four determinants. Learn the numbers to use for your determinants.

### 7. Solving Systems of Nonlinear Equations in Two Variables

In this lesson, we will take a look at how to solve non-linear systems of equations in two variables by exploring two solving techniques for these types of systems - graphing and substitution.

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### Other Chapters

Other chapters within the NES Mathematics (304): Practice & Study Guide course

- NES Math: Properties of Real Numbers
- NES Math: Fractions
- NES Math: Decimals & Percents
- NES Math: Ratios & Proportions
- NES Math: Units of Measure & Conversions
- NES Math: Logic
- NES Math: Reasoning
- NES Math: Vector Operations
- NES Math: Matrix Operations & Determinants
- NES Math: Exponents & Exponential Expressions
- NES Math: Algebraic Expressions
- NES Math: Linear Equations
- NES Math: Inequalities
- NES Math: Absolute Value
- NES Math: Quadratic Equations
- NES Math: Polynomials
- NES Math: Rational Expressions
- NES Math: Radical Expressions
- NES Math: Complex Numbers
- NES Math: Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- NES Math: Continuity of Functions
- NES Math: Limits
- NES Math: Rate of Change
- NES Math: Derivative Rules
- NES Math: Graphing Derivatives
- NES Math: Applications of Derivatives
- NES Math: Area Under the Curve & Integrals
- NES Math: Integration Techniques
- NES Math: Applications of Integration
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- NES Math: Properties of Triangles
- NES Math: Triangle Theorems & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Quadrilaterals
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- NES Math: Trigonometric Functions
- NES Math: Trigonometric Graphs
- NES Math: Solving Trigonometric Equations
- NES Math: Trigonometric Identities
- NES Math: Sequences & Series
- NES Math: Graph Theory
- NES Math: Set Theory
- NES Math: Statistics Overview
- NES Math: Summarizing Data
- NES Math: Tables, Plots & Graphs
- NES Math: Probability
- NES Math: Discrete Probability Distributions
- NES Math: Continuous Probability Distributions
- NES Math: Sampling
- NES Math: Regression & Correlation