# Ch 8: Systems of Equations & Inequalities

### About This Chapter

## Systems of Equations & Inequalities - Chapter Summary

Our professional instructors outline systems of equations and inequalities for your review in this chapter. You'll watch videos about solving systems of equations by elimination and graphing systems of inequalities. Once you complete this chapter, you should be ready to do the following:

- Explain what a system of equations is and how it's used
- Use two variables to solve a system of linear equations
- Solve a system of equations by graphing
- Understand how to solve nonlinear systems with a quadratic and a linear equation
- Outline the intersections of the graphs of two equations as solutions
- Identify the concept of graphing a system of inequalities

In this chapter, you'll find the resources you need to get ready to take an important exam. The mobile-friendly lessons are designed for flexible study and are accessible at any time. Help is available through the Dashboard if you have any questions come up as you progress through this chapter.

### 1. What is a System of Equations?

So what happens if we want to compare more than one equation? Welcome to a 'system' of equations! Learn what one is, how to solve them and when they come up in real life.

### 2. How Do I Use a System of Equations?

There are a few classic algebra word problems, such as the one about two trains traveling at different speeds. In this lesson, you'll learn how to take a word problem and convert it into the system of equations that will allow you to find the answer using either substitution or elimination.

### 3. How to Solve a System of Equations by Elimination

After watching this video lesson, you will have learned how to solve a system of equations by using the elimination method. You will learn what is being eliminated and how to do it so that you end with your solution.

### 4. 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.

### 5. How to Solve a System of Equations by Graphing

Watch this video lesson to learn how you can solve a system of equations by graphing. Learn when you have a solution and when you don't. Also learn how easy the solution is to spot.

### 6. Solving Nonlinear Systems with a Quadratic & a Linear Equation

In this lesson, we'll learn how to solve non-linear systems with a quadratic and linear equation both algebraically and graphically. We'll also look at the different possible solutions for this type of system.

### 7. Intersections of the Graphs of Two Equations as Solutions

This lesson will do a quick review of equations and their graphs and solutions. We will then look at intersections of graphs of two equations and see how these intersections actually represent solutions to the equations.

### 8. System of Inequalities: Graphing & Concept

When we need to solve a system of two or more inequalities, we graph the solution set of each one, but we put them on the same graph and see what that looks like. The overlapping shaded areas tells us where to find the solution set.

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### Other Chapters

Other chapters within the Praxis Algebra I (5162): Study Guide & Practice course

- Algebraic Expressions
- Solving Algebraic Equations with One or More Variables
- Algebraic Inequalities
- Arithmetic Operations & Polynomials
- Calculating Slope, Intercept & Rate of Change
- Basics of Linear Equations
- Overview of Quadratic Equations
- Fundamentals of Functions
- Analyzing Behavior of Functions
- Explicit & Recursive Functions
- Transformations, Composite Functions & Inverse Functions
- Modeling with Functions
- Exponents & Order of Magnitude
- Basics of Rational & Irrational Numbers
- Measurements, Reasonableness & Accuracy
- Data Analysis: Graphical & Statistical
- Scatterplots & Correlation
- Praxis Algebra I (5162) Flashcards