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

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Atiya

30/03/2023

Maths

Simultaneous equations

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Solving Systems of Equations with Elimination

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Systems of Equations with Elimination: X-4Y=-18 & -X+3Y=11

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

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
...

30/03/2023

75

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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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

Systems of Equations with Elimination: X-4Y=-18 & -X+3Y=11

 

Maths

•

75

•

30 Mar 2023

•

2 pages

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

user profile picture

Atiya

@atiya.kw

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... Show more

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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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.

Sign up to see the contentIt'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.

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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.

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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.

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Best app on earth! no words because it’s too good

Thomas R

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Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

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This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

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very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

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I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

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THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

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This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

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