Back To Course

High School Algebra II: Tutoring Solution26 chapters | 274 lessons

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

What does the substitution method have to do with substitute teachers? Learn why you should love substitutes. Also learn how substitutes make your life easier when it comes to solving sets of equations.

It shouldn't give you a headache. Really, it shouldn't. The **substitution method** helps you to solve your problems by substituting simpler things into your equation so you can solve the problem faster and without difficulty. Just like real-world substitutes take the place of your teacher and make your life a little bit easier for the day, the same goes for the substitution method. Also, similar to the way substitute teachers give you direction while your teacher is gone, the substitution method gives you a clearer idea of how to solve the problem when the answer is not present.

To give you an idea of how substitution works, let's say that I have some nickels and dimes. I want to figure out how many nickels and dimes it takes to make a quarter. Okay, so you have probably already figured out that it takes two dimes and one nickel. But let's say that I didn't know that. Let's say that the only things I did know was that I had nickels and dimes and that it takes two nickels to make a dime. Instead of trying to figure out how many dimes and nickels I need, I can much more easily try to figure out how many nickels I need if I replace every dime with two nickels. I figure out the number of nickels by dividing 25 by 5. Doing that, I get 5 nickels. But wait, I know that I can replace two nickels with a dime, so how many dimes can I substitute back in? I can switch four of the nickels out and I will have two dimes. And voila, I have my answer. It takes two dimes and one nickel to make a quarter. See how it works?

Substitution is usually used in systems of equations. If you are given a word problem, you first need to write it as a system of equations. Remember our example of the nickels and dimes? How would you write that as a system of equations? I would start by defining my variables. I will label my dimes *d* and my nickels *n*. In this example, I end up with two equations: one that gives me the number of nickels and dimes it takes to make a quarter and another that tells me how many nickels are in a dime. My two equations are *10d+5n=25* and *d=2n*. Notice how I've multiplied the dimes by 10 and the nickels by 5 in the first equation? I did this because I need to know how many pennies are in each group. I know that dimes are 10 cents each and nickels are 5 cents each. So, to figure out how many pennies are in each, I multiply.

Looking at the first equation, I notice that I have two variables. Hmmm - I can't solve that because I have more variables than I know what to do with. But, looking at the second equation, I see that I can substitute *2n* for the *d*. Doing that, my first equation becomes *10(2n)+5n=25*. I can definitely solve this for *n*. Let's see what we get.

10(2n)+5n=25 | I multiply the 10 and 2 |

20n+5n=25 | Combine like terms |

25n=25 | Divide by 25 on both sides |

n=1 | I get one nickel |

This tells me that I need one nickel. To figure out the number of dimes, I plug my *n=1* into the second equation. This is what I get.

d=2n |

d=2(1) |

d=2 |

So I need two dimes. So my final answer is two dimes and one nickel to make a quarter. While the math problems you see may seem harder, they really aren't. Just remember how easy this was. You are doing the exact same steps, only the variables might be different.

If you happen to have three variables instead of two, just do what you just learned. The only major difference is that you need a third equation to tell you what to substitute for the third variable. Remember, the only way to solve an equation is if it only has one variable. So that is your goal - to substitute other equations for the unknown variables so that you are left with only one variable. For example, let's say your math problem had *x*, *y*, and *z* as variables. You see that the second equation gives you *y* in terms of *x* and the third equation gives you *z* in terms of *x*. Well, you could substitute those equations into the first so that the only variable it has is *x*. Once you've solved for the *x*, you can use that information to solve for the other variables.

The substitution method is not as hard as it may first appear to be. Remember that your goal is to simplify your life. You know that to solve an equation, it can only have one variable. Make that your goal when looking at the other equations in the problem. You want to use an equation where you can substitute or rewrite an unknown variable in terms of the variable you want to solve for.

After finishing this lesson, you should be able to:

- Describe the substitution method
- Explain how to use substitution to solve equations
- Solve examples by using the substitution method

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
7 in chapter 8 of the course:

Back To Course

High School Algebra II: Tutoring Solution26 chapters | 274 lessons

- What is a System of Equations? 8:39
- How Do I Use a System of Equations? 9:47
- How to Solve a System of Linear Equations in Two Variables 4:43
- How to Solve a Linear System in Three Variables With a Solution 5:01
- How to Solve a Linear System in Three Variables With No or Infinite Solutions 6:04
- Gaussian Elimination: Method & Examples
- Solving Equations with the Substitution Method: Algebra Examples & Overview
- Go to Algebra II - Systems of Linear Equations: Tutoring Solution

- Computer Science 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- TExES Chemistry: Equipment, Safety & Measurements
- MTLE Life Science: Using Statistics
- Important Events in the US (1954-1980)
- Martin Luther & The Protestant Reformation in Europe
- Early Civilizations & The Ancient Near East
- CEOE Test Cost
- PHR Exam Registration Information
- Claiming a Tax Deduction for Your Study.com Teacher Edition
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP

- Displacement Current: Definition & Function
- Finding the Basis of a Vector Space
- Time Series Analysis & Its Applications
- Diazonium Salts: Preparation & Chemical Reactions
- Ecosystem Project Ideas for 5th Grade
- Book Timeline Project Ideas
- Biography Project Ideas for High School
- Quiz & Worksheet - Syn & Anti Addition in Stereochemistry
- Quiz & Worksheet - Asymmetric Carbons
- Quiz & Worksheet - Osteoporosis & Osteomalacia Comparison
- Quiz & Worksheet - Cumulative Distribution Function Calculation
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Social and Emotional Learning | Self-Management
- Analytical Essay Topics for Teachers

- AP World History: Help and Review
- History of World War 2 Study Guide
- NYSTCE Physics (009): Practice and Study Guide
- Post-Civil War American History: Homework Help
- Middle School Life Science: Tutoring Solution
- Enzymes and Metabolism for the MCAT: Tutoring Solution
- Structure, Function & Sensory Reception in the Nervous System for the MCAT: Tutoring Solution
- Quiz & Worksheet - Human Behavior
- Quiz & Worksheet - How Genetics and Environment Influence Human Behavior
- Quiz & Worksheet - Movement of Fluids
- Quiz & Worksheet - Global Energy Uses & Needs
- Quiz & Worksheet - Resultants of Vectors

- What is Standardized Testing? - Definition & Types
- Extinct Animal Facts: Lesson for Kids
- Average LSAT Score
- DNA Model Project Ideas
- 5th Grade Science Projects
- What is a Good PSAT Score for a Junior?
- Introduction to Western Civilization II Course
- Place Value Lesson Plan
- Speed Reading for Kids
- Best Apps for the Classroom
- Study.com for Enterprise
- The Taming of the Shrew Lesson Plan

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

Browse by subject