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

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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.

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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

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