# Ch 8: Solving Problems with Systems of Equations

### About This Chapter

## Solving Problems with Systems of Equations - Chapter Summary

If you need help studying how to solve problems with systems of equations, look no further! This self-paced chapter provides a comprehensive overview of this subject by delving into ways to use systems of equations, solve linear equations and more. Complete the lessons to enhance your ability to:

- Define, graph and use a system of equations
- Explain why intersections of the graphs of two equations are solutions
- Graph to solve linear equations
- Solve linear equations with substitution
- Use linear combinations to solve systems of equations

The lessons in this chapter are available around-the-clock, enabling you to study ways to solve problems with systems of equations whenever your schedule permits. Access any number of lessons in this chapter and visit them as often as you'd like to boost your knowledge of this subject. When ready, test your knowledge of the lessons you review by taking mini quizzes. A practice exam can check your understanding of the entire 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. 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.

### 4. How to Solve Linear Equations By Graphing

This lesson will give a quick review of systems of linear equations and their solutions. We will then look at taking an example through a step-by-step process that allows us to solve a system of linear equations by graphing.

### 5. Solving Linear Equations With Substitution

Solving for the unknowns in a set of linear equations is a common task in math, science and engineering. In this lesson, we look at the substitution method as a systematic approach to finding the unknown values.

### 6. Solving Systems of Equations with Linear Combinations

This lesson will show how to solve Systems of Equations with Linear Combinations. We will use some sample problems and properties to prove the solution is the point of intersection.

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### Other Chapters

Other chapters within the Pennsylvania Algebra I Keystone Exam: Test Prep & Practice course

- Real Numbers & Expressions
- Understanding Exponential Expressions
- Working with Radical Expressions
- Understanding Absolute Value Expressions
- Estimation & Math Problem-Solving
- Solving Problems with Polynomials
- Solving, Writing & Graphing Linear Equations
- Solving & Graphing Linear Inequalities
- Understanding Function Basics
- Using Scatter Plots
- Understanding Basic Statistics
- Interpreting & Graphing Data
- Understanding the Probability of Compound Events
- Pennsylvania Algebra I Keystone Exam Flashcards