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Step-by-Step Guide to Solving Simultaneous Equations: Examples, Methods, and Answers

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Step-by-Step Guide to Solving Simultaneous Equations: Examples, Methods, and Answers
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Atiya

@atiya.kw

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Solving Simultaneous Equations: A Comprehensive Guide

This guide provides a detailed explanation of how to solve simultaneous equations by substitution and other methods. It covers step-by-step processes, examples, and key techniques for tackling various types of simultaneous equations problems.

  • Introduces the concept of simultaneous equations with practical examples
  • Outlines multiple methods for solving, including substitution and elimination
  • Provides detailed steps and explanations for each solving technique
  • Includes worked examples to illustrate the application of these methods

3/30/2023

72

Maths - Simultanious equations. E.g. 5x+3y=41 2x+3y=20 Зу 5x -20c are Same = 3x 21 41-20 3x = 21 2x7 + 3y = 20 14+3y=20 -14 So So they cance

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Understanding Simultaneous Equations

Simultaneous equations are a set of equations that must be solved together to find values that satisfy all equations simultaneously. This page introduces the concept with a practical example and outlines the steps for solving such equations.

Example: The guide presents two simultaneous equations: 5x + 3y = 41 2x + 3y = 20

The solving process begins by identifying common terms between the equations. In this case, the 3y term is present in both equations, which can be used as a starting point for solving.

Highlight: The key to solving simultaneous equations is to manipulate the equations to eliminate one variable, allowing you to solve for the other.

The page outlines six steps for solving simultaneous equations:

  1. Cancel out terms
  2. Subtract terms
  3. Subtract y or x terms
  4. Divide the answer by the term's coefficient
  5. Multiply the answer by the initial term
  6. Cancel out any extra terms

Vocabulary: Elimination method simultaneous equations refers to the process of removing one variable by adding or subtracting equations to simplify the problem.

These steps form the foundation of the elimination method, which is one of the three methods of solving simultaneous equations commonly taught in schools.

Maths - Simultanious equations. E.g. 5x+3y=41 2x+3y=20 Зу 5x -20c are Same = 3x 21 41-20 3x = 21 2x7 + 3y = 20 14+3y=20 -14 So So they cance

View

Applying the Solving Technique

This page demonstrates the application of the solving steps introduced earlier, providing a detailed walkthrough of solving a set of simultaneous equations.

The example used is: 28 + 2c = 18 38 + 2c = 22

Example: The solving process is shown step-by-step:

  1. Subtract 2c from both equations to eliminate the variable c
  2. This results in: 28 - 38 = -5 and 18 - 22 = -4
  3. Solve for c: 2c = 10, so c = 5

Highlight: The substitution method is implicitly used here, as the value of c is then substituted back into one of the original equations to verify the solution.

This example illustrates how the simultaneous equations solver approach can be applied to real problems, providing students with a clear demonstration of the technique in action.

Definition: Substitution in simultaneous equations involves using the value of one variable found from one equation in the other equation to solve for the remaining variable.

By working through this example, students can see how the abstract steps translate into a practical problem-solving method, reinforcing their understanding of how to solve simultaneous equations step by step.

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Subjects

/

Maths

/

Systems of equations

/

Solving systems of equations with elimination

Step-by-Step Guide to Solving Simultaneous Equations: Examples, Methods, and Answers

user profile picture

Atiya

@atiya.kw

·

2 Followers

Follow

Solving Simultaneous Equations: A Comprehensive Guide

This guide provides a detailed explanation of how to solve simultaneous equations by substitution and other methods. It covers step-by-step processes, examples, and key techniques for tackling various types of simultaneous equations problems.

  • Introduces the concept of simultaneous equations with practical examples
  • Outlines multiple methods for solving, including substitution and elimination
  • Provides detailed steps and explanations for each solving technique
  • Includes worked examples to illustrate the application of these methods

3/30/2023

72

 

10/9

 

Maths

4

Maths - Simultanious equations. E.g. 5x+3y=41 2x+3y=20 Зу 5x -20c are Same = 3x 21 41-20 3x = 21 2x7 + 3y = 20 14+3y=20 -14 So So they cance

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Understanding Simultaneous Equations

Simultaneous equations are a set of equations that must be solved together to find values that satisfy all equations simultaneously. This page introduces the concept with a practical example and outlines the steps for solving such equations.

Example: The guide presents two simultaneous equations: 5x + 3y = 41 2x + 3y = 20

The solving process begins by identifying common terms between the equations. In this case, the 3y term is present in both equations, which can be used as a starting point for solving.

Highlight: The key to solving simultaneous equations is to manipulate the equations to eliminate one variable, allowing you to solve for the other.

The page outlines six steps for solving simultaneous equations:

  1. Cancel out terms
  2. Subtract terms
  3. Subtract y or x terms
  4. Divide the answer by the term's coefficient
  5. Multiply the answer by the initial term
  6. Cancel out any extra terms

Vocabulary: Elimination method simultaneous equations refers to the process of removing one variable by adding or subtracting equations to simplify the problem.

These steps form the foundation of the elimination method, which is one of the three methods of solving simultaneous equations commonly taught in schools.

Maths - Simultanious equations. E.g. 5x+3y=41 2x+3y=20 Зу 5x -20c are Same = 3x 21 41-20 3x = 21 2x7 + 3y = 20 14+3y=20 -14 So So they cance

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Applying the Solving Technique

This page demonstrates the application of the solving steps introduced earlier, providing a detailed walkthrough of solving a set of simultaneous equations.

The example used is: 28 + 2c = 18 38 + 2c = 22

Example: The solving process is shown step-by-step:

  1. Subtract 2c from both equations to eliminate the variable c
  2. This results in: 28 - 38 = -5 and 18 - 22 = -4
  3. Solve for c: 2c = 10, so c = 5

Highlight: The substitution method is implicitly used here, as the value of c is then substituted back into one of the original equations to verify the solution.

This example illustrates how the simultaneous equations solver approach can be applied to real problems, providing students with a clear demonstration of the technique in action.

Definition: Substitution in simultaneous equations involves using the value of one variable found from one equation in the other equation to solve for the remaining variable.

By working through this example, students can see how the abstract steps translate into a practical problem-solving method, reinforcing their understanding of how to solve simultaneous equations step by step.

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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