The solving systems of linear equations using elimination method is...
Algebra 1437 views·Updated Jun 10, 2026·2 pagesFun with Elimination Method: Worksheets & Examples for Solving Equations
1
of 2
More Elimination Method Examples
This page continues with additional elimination method examples, demonstrating various scenarios and techniques for solving systems of linear equations.
Example 1: Solve: -9x + 8y = 2 2x + 8y = -20
In this case, the 8y terms can be eliminated by subtracting the equations. The process involves:
- Subtracting the equations to eliminate 8y
- Solving for x
- Substituting x to solve for y
The solution for this system is (-2, -2).
Example 2: Solve: -9x + 8y = 2 2x + 8y = -20 -4y - 6x + 26 = 0 4y = 3x - 19
This more complex example involves multiple equations. The strategy here is to:
- Choose two equations that allow for easy elimination
- Solve for one variable
- Use substitution to find the other variable
Highlight: When dealing with multiple equations, select the pair that allows for the simplest elimination process.
The solution for this system is (5, -1).
Vocabulary: Coefficient - The numerical factor of a term in an algebraic expression.
These examples demonstrate the versatility of the elimination method in solving various types of systems of linear equations, from simple two-equation systems to more complex multi-equation problems.
2
of 2
Solving Systems of Linear Equations using Elimination
This page introduces the elimination method for solving systems of linear equations in Algebra 1. The elimination method is an algebraic approach that involves eliminating one variable to simplify the problem-solving process.
Definition: The elimination method is a technique for solving systems of two linear equations by adding or subtracting the equations to eliminate one variable.
Key requirements for using the elimination method include:
- Equations must be precisely lined up, with x's aligned with x's, y's with y's, and equal signs with equal signs.
- Coefficients of one set of variables must be the same (positive or negative doesn't matter).
Example: Properly aligned equations: 3x + 2y = 7 -4x + y = -1
Example: Improperly aligned equations: y = 1 5x + 4y = 7
The page provides step-by-step elimination method examples to illustrate the process:
- Solve: 3x - 2y = -8 -3x + 4y = 10
In this example, the 3x terms can be eliminated by adding the equations. The solution process involves:
- Adding the equations to eliminate 3x
- Solving for y
- Substituting y to solve for x
- Checking the solution
Highlight: The key to successful elimination is identifying which operation (addition or subtraction) will eliminate a variable.
The final solution for this system is (-2, 1).
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar Content
MathsMost popular content: Elimination Method
1Most popular content in Algebra 1
9M
Algebra 1Mastering Algebra 1: Essential Flashcards
Learn key concepts of Algebra 1 with these flashcards. Explore slope-intercept form, properties, equations, and expressions. Boost your math skills and ace your exams!
8th1811
7
Algebra 17th Grade Math
Algebra 1 and all of the other stuff
7th4194
W
Algebra 1wizards
Mathematics is the most loved and also the most feared subjects by students across the world. Have you been worrying about your upcoming math test? Practice these 30 maths quiz questions to ensure you are at the top of your game!
980
Algebra 1Interior and exterior angle measures
Interior and exterior angle measures practice
9th2721
Algebra 1Expressions and Operations
Algebra 1 - unit 1 - covers: integer rules, order of operations, evaluating algerbraic expressions, simplifying algebraic expressions, and translating expressions.
9th1,46195
Algebra 1Math study guide: linear equations, standard form,proportional relationships, & dimensional analysis
This study guide shows you through all things about point-slope formula of a linear equation, and all the forms of a linear equation, as well as explaining the process of dimensional analysis.
9th821
Algebra 1Linear Function: Solving Linear Equations in 1 Variable
Study note on linear equations with one variable, rules on linear equations, examples on simple linear equations, algebra 2, algebra 1
9th3321
Algebra 1Solving leaner equations
About the topic
1739
Algebra 1Order Of Operations
PEMDAS (GEMDAS)
9th1521
Most popular content
9O
AP US HistoryOrigins and Dynamics of the Columbian Exchange
Analyze the ecological and economic motivations behind the initial transfer of goods, people, and diseases between the Old and New Worlds.
9th3,1280
I
AP US HistoryIntroduction to Early Cultural Interactions
Analyze the initial social and religious encounters between Europeans, Africans, and Indigenous peoples in the colonial Americas.
9th2,7730
O
AP World HistoryOrigins of Ancient River Civilizations
Analyze the environmental factors and technological innovations that led to the rise of early states in Mesopotamia, Egypt, and the Indus Valley.
9th3,1870
M
AP US HistoryMotivations for European Exploration
Analyze the economic, religious, and political factors that drove European powers to the Americas during the 15th and 16th centuries.
9th1,7780
F
AP PsychologyFoundations of Ethical Guidelines in Research
Practice the core principles of the APA ethical code including informed consent, debriefing, and the role of Institutional Review Boards.
9th1,3360
I
AP US HistoryIntroduction to Native American Societies
Examine the diverse social, political, and economic structures of North American indigenous groups prior to European contact.
9th1,1100
I
AP BiologyIntroduction to Biological Elements of Life
Practice identifying the essential elements including carbon, nitrogen, phosphorus, and sulfur that compose biological macromolecules.
9th1,7390
I
AP US HistoryIntroduction to the Spanish Encomienda System
Explore the fundamental economic and social structures of the Spanish colonial system, focusing on the encomienda and the casta social hierarchy.
9th8890
O
AP World HistoryOrigins and Continuity of the Byzantine Empire
Analyze the political and cultural transitions from the Roman Empire to the Byzantine Empire, focusing on the reign of Justinian I and his code.
9th1,6320
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user
Algebra 1437 views·Updated Jun 10, 2026·2 pagesFun with Elimination Method: Worksheets & Examples for Solving Equations
The solving systems of linear equations using elimination method is a powerful algebraic technique for solving systems of two linear equations. This method involves strategically eliminating one variable to simplify the problem-solving process. Elimination method examplesdemonstrate how to align...
1
of 2
Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
More Elimination Method Examples
This page continues with additional elimination method examples, demonstrating various scenarios and techniques for solving systems of linear equations.
Example 1: Solve: -9x + 8y = 2 2x + 8y = -20
In this case, the 8y terms can be eliminated by subtracting the equations. The process involves:
- Subtracting the equations to eliminate 8y
- Solving for x
- Substituting x to solve for y
The solution for this system is (-2, -2).
Example 2: Solve: -9x + 8y = 2 2x + 8y = -20 -4y - 6x + 26 = 0 4y = 3x - 19
This more complex example involves multiple equations. The strategy here is to:
- Choose two equations that allow for easy elimination
- Solve for one variable
- Use substitution to find the other variable
Highlight: When dealing with multiple equations, select the pair that allows for the simplest elimination process.
The solution for this system is (5, -1).
Vocabulary: Coefficient - The numerical factor of a term in an algebraic expression.
These examples demonstrate the versatility of the elimination method in solving various types of systems of linear equations, from simple two-equation systems to more complex multi-equation problems.
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Solving Systems of Linear Equations using Elimination
This page introduces the elimination method for solving systems of linear equations in Algebra 1. The elimination method is an algebraic approach that involves eliminating one variable to simplify the problem-solving process.
Definition: The elimination method is a technique for solving systems of two linear equations by adding or subtracting the equations to eliminate one variable.
Key requirements for using the elimination method include:
- Equations must be precisely lined up, with x's aligned with x's, y's with y's, and equal signs with equal signs.
- Coefficients of one set of variables must be the same (positive or negative doesn't matter).
Example: Properly aligned equations: 3x + 2y = 7 -4x + y = -1
Example: Improperly aligned equations: y = 1 5x + 4y = 7
The page provides step-by-step elimination method examples to illustrate the process:
- Solve: 3x - 2y = -8 -3x + 4y = 10
In this example, the 3x terms can be eliminated by adding the equations. The solution process involves:
- Adding the equations to eliminate 3x
- Solving for y
- Substituting y to solve for x
- Checking the solution
Highlight: The key to successful elimination is identifying which operation (addition or subtraction) will eliminate a variable.
The final solution for this system is (-2, 1).
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar Content
Most popular content: Elimination Method
1Most popular content in Algebra 1
9M
Algebra 1Mastering Algebra 1: Essential Flashcards
Learn key concepts of Algebra 1 with these flashcards. Explore slope-intercept form, properties, equations, and expressions. Boost your math skills and ace your exams!
8th1811
7
Algebra 17th Grade Math
Algebra 1 and all of the other stuff
7th4194
W
Algebra 1wizards
Mathematics is the most loved and also the most feared subjects by students across the world. Have you been worrying about your upcoming math test? Practice these 30 maths quiz questions to ensure you are at the top of your game!
980
Algebra 1Interior and exterior angle measures
Interior and exterior angle measures practice
9th2721
Algebra 1Expressions and Operations
Algebra 1 - unit 1 - covers: integer rules, order of operations, evaluating algerbraic expressions, simplifying algebraic expressions, and translating expressions.
9th1,46195
Algebra 1Math study guide: linear equations, standard form,proportional relationships, & dimensional analysis
This study guide shows you through all things about point-slope formula of a linear equation, and all the forms of a linear equation, as well as explaining the process of dimensional analysis.
9th821
Algebra 1Linear Function: Solving Linear Equations in 1 Variable
Study note on linear equations with one variable, rules on linear equations, examples on simple linear equations, algebra 2, algebra 1
9th3321
Algebra 1Solving leaner equations
About the topic
1739
Algebra 1Order Of Operations
PEMDAS (GEMDAS)
9th1521
Most popular content
9O
AP US HistoryOrigins and Dynamics of the Columbian Exchange
Analyze the ecological and economic motivations behind the initial transfer of goods, people, and diseases between the Old and New Worlds.
9th3,1280
I
AP US HistoryIntroduction to Early Cultural Interactions
Analyze the initial social and religious encounters between Europeans, Africans, and Indigenous peoples in the colonial Americas.
9th2,7730
O
AP World HistoryOrigins of Ancient River Civilizations
Analyze the environmental factors and technological innovations that led to the rise of early states in Mesopotamia, Egypt, and the Indus Valley.
9th3,1870
M
AP US HistoryMotivations for European Exploration
Analyze the economic, religious, and political factors that drove European powers to the Americas during the 15th and 16th centuries.
9th1,7780
F
AP PsychologyFoundations of Ethical Guidelines in Research
Practice the core principles of the APA ethical code including informed consent, debriefing, and the role of Institutional Review Boards.
9th1,3360
I
AP US HistoryIntroduction to Native American Societies
Examine the diverse social, political, and economic structures of North American indigenous groups prior to European contact.
9th1,1100
I
AP BiologyIntroduction to Biological Elements of Life
Practice identifying the essential elements including carbon, nitrogen, phosphorus, and sulfur that compose biological macromolecules.
9th1,7390
I
AP US HistoryIntroduction to the Spanish Encomienda System
Explore the fundamental economic and social structures of the Spanish colonial system, focusing on the encomienda and the casta social hierarchy.
9th8890
O
AP World HistoryOrigins and Continuity of the Byzantine Empire
Analyze the political and cultural transitions from the Roman Empire to the Byzantine Empire, focusing on the reign of Justinian I and his code.
9th1,6320
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user