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Substitution Property of Equality: Definition & Examples

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  • 0:00 Substitution Property…
  • 0:31 Why Is It Important?
  • 1:10 Examples
  • 2:32 Lesson Summary
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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.

Substitution Property of Equality

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.

Why is It Important?

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.

Examples

Example 1:

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

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

Example 2:

Let's look at the expression:

4x + 5y + 2p

We know that:

x = 2

y = 1

p = 3

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