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Easy Steps to Solve Systems of Equations: Elimination and Substitution

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Easy Steps to Solve Systems of Equations: Elimination and Substitution
user profile picture

Asiya

@ciya

·

10 Followers

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A comprehensive guide to solving system of equations elimination method steps and substitution techniques in algebra.

  • Learn two primary methods for solving systems of linear equations: elimination and substitution
  • Master the systematic approach to solving equations through detailed step-by-step instructions
  • Understand how to verify solutions and check work for accuracy
  • Practice with multiple example problems for solving linear equations across varying difficulty levels
  • Gain proficiency in how to solve system of equations using substitution through structured learning

8/18/2023

72

System of Equations - Elimination (4.1) 1/31/23 1. Place both equations in standard form. Ax + By = C 12. Determine which variable to elimin

View

Page 1: System of Equations - Elimination Method

The elimination method follows a structured approach to solving systems of equations by strategically removing variables. This page outlines the fundamental steps and provides practical examples.

Definition: The elimination method involves manipulating two equations to cancel out one variable, allowing you to solve for the remaining variable.

Highlight: The five key steps for elimination method are:

  1. Write equations in standard form
  2. Choose variable to eliminate
  3. Solve for remaining variable
  4. Substitute to find second variable
  5. Verify solution

Example: Consider the system: 5x + 2y = 1 5x + 3y = 11 By subtracting equations, we eliminate x and solve for y=2

System of Equations - Elimination (4.1) 1/31/23 1. Place both equations in standard form. Ax + By = C 12. Determine which variable to elimin

View

Page 3: Substitution Method

The substitution method offers an alternative approach to solving systems of equations by expressing one variable in terms of another.

Definition: Substitution involves solving for one variable in terms of another and replacing it in the second equation.

Example: For the system: 2x + 3y = 10 5x - y = 2 Solve by expressing y in terms of x: y = -x + 10

Highlight: The substitution method is particularly useful when:

  • One variable has a coefficient of 1
  • One equation is already solved for a variable
  • Direct elimination would be more complicated
System of Equations - Elimination (4.1) 1/31/23 1. Place both equations in standard form. Ax + By = C 12. Determine which variable to elimin

View

Page 2: Advanced Elimination Examples

This page demonstrates more complex applications of the elimination method, showing how to handle equations with different coefficients and variables.

Vocabulary: LCM (Least Common Multiple) - Used when coefficients need to be matched for elimination

Example: For the system: 2x + 4y = 1 2x - y = 6 Solve by first aligning coefficients of x, then subtracting equations

Highlight: When working with fractions, multiply equations by appropriate factors to create whole numbers before elimination

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SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

/

Algebra 2

/

Modeling

/

Modeling with two variables

Easy Steps to Solve Systems of Equations: Elimination and Substitution

user profile picture

Asiya

@ciya

·

10 Followers

Follow

A comprehensive guide to solving system of equations elimination method steps and substitution techniques in algebra.

  • Learn two primary methods for solving systems of linear equations: elimination and substitution
  • Master the systematic approach to solving equations through detailed step-by-step instructions
  • Understand how to verify solutions and check work for accuracy
  • Practice with multiple example problems for solving linear equations across varying difficulty levels
  • Gain proficiency in how to solve system of equations using substitution through structured learning

8/18/2023

72

 

9th/10th

 

Algebra 2

3

System of Equations - Elimination (4.1) 1/31/23 1. Place both equations in standard form. Ax + By = C 12. Determine which variable to elimin

Page 1: System of Equations - Elimination Method

The elimination method follows a structured approach to solving systems of equations by strategically removing variables. This page outlines the fundamental steps and provides practical examples.

Definition: The elimination method involves manipulating two equations to cancel out one variable, allowing you to solve for the remaining variable.

Highlight: The five key steps for elimination method are:

  1. Write equations in standard form
  2. Choose variable to eliminate
  3. Solve for remaining variable
  4. Substitute to find second variable
  5. Verify solution

Example: Consider the system: 5x + 2y = 1 5x + 3y = 11 By subtracting equations, we eliminate x and solve for y=2

System of Equations - Elimination (4.1) 1/31/23 1. Place both equations in standard form. Ax + By = C 12. Determine which variable to elimin

Page 3: Substitution Method

The substitution method offers an alternative approach to solving systems of equations by expressing one variable in terms of another.

Definition: Substitution involves solving for one variable in terms of another and replacing it in the second equation.

Example: For the system: 2x + 3y = 10 5x - y = 2 Solve by expressing y in terms of x: y = -x + 10

Highlight: The substitution method is particularly useful when:

  • One variable has a coefficient of 1
  • One equation is already solved for a variable
  • Direct elimination would be more complicated
System of Equations - Elimination (4.1) 1/31/23 1. Place both equations in standard form. Ax + By = C 12. Determine which variable to elimin

Page 2: Advanced Elimination Examples

This page demonstrates more complex applications of the elimination method, showing how to handle equations with different coefficients and variables.

Vocabulary: LCM (Least Common Multiple) - Used when coefficients need to be matched for elimination

Example: For the system: 2x + 4y = 1 2x - y = 6 Solve by first aligning coefficients of x, then subtracting equations

Highlight: When working with fractions, multiply equations by appropriate factors to create whole numbers before elimination

Similar Content

Algebra 2 - Understanding Polynomial Functions: Degree, Coefficients, and Behavior

alg 2 unit 4.1- Learn about polynomial functions, their degree, leading coefficients, and behavior at infinity and negative infinity.

3

43

0

Know Understanding Polynomial Functions: Degree, Coefficients, and Behavior thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying