Back To Course

High School Algebra II: Help and Review26 chapters | 296 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Karin Gonzalez*

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, you will learn the definition of the substitution property of equality and why this property is so important in mathematics. You will be given examples to illustrate.

The **substitution property of equality**, one of the eight properties of equality, states that if *x* = *y*, then *x* can be substituted in for *y* in any equation, and *y* can be substituted for *x* in any equation.

Let's look at a quick and simple example. If we know that *x* = *y* and we have the equation *x* + 5 = 7, then we can substitute *y* for *x* and write the equation as *y* + 5 = 7.

In short, the substitution property of equality makes algebra possible. If we did not use this property in algebra, we would not be able to plug in known values for variables into mathematical expressions and equations. Even though the property is pretty easy to comprehend, it is a big deal when it comes to mathematics, especially algebra!

And why is algebra important, you may ask? Algebra is the branch of mathematics that helps us find the unknown in a mathematical expression. Usually that 'unknown' number will be represented by a letter, like *x* or *y.* Algebra is so important because it allows us to take real life word problems and write them as mathematical expressions so that we can solve them.

Example 1:

Let's take a look at a very simple example to start. Let's say that we have 5*x* and we know that *x* = 5. We can use the substitution property of equality to plug in the value of *x* into 5*x*:

So we would get 5 x 5, which is 25!

Example 2:

Let's look at the expression:

4*x* + 5*y* + 2*p*

We know that:

*x* = 2

*y* = 1

*p* = 3

Using the substitution property of equality, we can plug the values of *x*, *y* and *p* into the expression to solve it!

(4 x 2) + (5 x 1) + (2 x 3) =

(8) + (5) + (6) = 19

We have solved the expression, and 19 is the answer!

Example 3:

Angle *a* = angle *c* and angle *a* + angle *b* = 90 degrees

Using the substitution property of equality, we infer that because angle *a* = angle *c*, that we can substitute angle *c* for angle *a* into the equation.

So, we can conclude that angle *c* + angle *b* = 90 degrees

Example 4:

6*y* + 5 when *y* = {3, 4, 5}

Here, *y* equals three values. To help us organize, we can make a table and plug in each of the three values into the expression.

Let's review. The **substitution property of equality** makes algebra possible. Remember that it states that if *x* = *y*, then *x* can be substituted in for *y* in any equation, and *y* can be substituted for *x* in any equation. It is very important; without it, we would not be able to plug in known values for variables into mathematical expressions and equations.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
23 in chapter 2 of the course:

Back To Course

High School Algebra II: Help and Review26 chapters | 296 lessons

- What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions 5:50
- Understanding and Evaluating Math Formulas 7:08
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- Combining Like Terms in Algebraic Expressions 7:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Writing Equations with Inequalities: Open Sentences and True/False Statements 4:22
- Common Algebraic Equations: Linear, Quadratic, Polynomial, and More 7:28
- Defining, Translating, & Solving One-Step Equations 6:15
- Solving Equations Using the Addition Principle 5:20
- Solving Equations Using the Multiplication Principle 4:03
- Solving Equations Using Both Addition and Multiplication Principles 6:21
- Collecting Like Terms On One Side of an Equation 6:28
- Solving Equations Containing Parentheses 6:50
- Translating Words to Algebraic Expressions 6:31
- How to Solve One-Step Algebra Equations in Word Problems 5:05
- How to Solve Equations with Multiple Steps 5:44
- How to Solve Multi-Step Algebra Equations in Word Problems 6:16
- Distributive Property: Definition, Use & Examples 6:20
- Vector Space Model: Examples
- Solving Complex Equations: Examples & Explanation 4:06
- Substitution Property of Equality: Definition & Examples 2:57
- Go to Algebra II - Algebraic Expressions: Help & Review

- AFOQT Information Guide
- ACT Information Guide
- Computer Science 335: Mobile Forensics
- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- FTCE Middle Grades Math: Connecting Math Concepts
- Social Justice Goals in Social Work
- Developmental Abnormalities
- Overview of Human Growth & Development
- ACT Informational Resources
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- How to Write a Newspaper Article
- Anthem by Ayn Rand: Book Summary
- Field Hockey: Techniques, Rules & Skills
- What's the Difference Between Polytheism and Monotheism?
- Martin Luther King Jr. Activities for Middle School
- Age of Exploration Project Ideas
- Fast Food Nation Discussion Questions
- Quiz & Worksheet - Who, What, When, Where & Why
- Quiz & Worksheet - American Ethnic Groups
- Quiz & Worksheet - Kinds of Color Wheels
- Quiz & Worksheet - Phenol Reactions
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- 3rd Grade Math Worksheets & Printables
- Geometry Worksheets

- Statistics for Teachers: Professional Development
- Investing: Help & Tutorials
- AP Environmental Science: Tutoring Solution
- High School Trigonometry: Help and Review
- Common Core Math - Geometry: High School Standards
- American Imperialism & World War l: Help and Review
- Critical Reasoning for Test-Taking: Help and Review
- Quiz & Worksheet - Barrier Methods of Contraception
- Quiz & Worksheet - Features of Taigas
- Quiz & Worksheet - Autopsy Procedure & Results
- Quiz & Worksheet - Random Assortment of Chromosomes
- Quiz & Worksheet - Cutaneous Breathing in Amphibians

- Arctic Food Chain
- Abscess: Definition, Symptoms & Treatment
- 6th Grade South Carolina Science Standards
- Narrative Writing Lesson Plan
- Letter Writing Lesson Plan
- 8th Grade Florida Science Standards
- Maryland State Standards for Science
- Middle Ages Lesson Plan
- Teacher Retirement System of Texas Withdrawal
- TExES PPR Test Dates
- Andrew Jackson Lesson Plan
- Things Fall Apart Lesson Plan

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject