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

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Atiya

3/30/2023

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
...

3/30/2023

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

•

Mar 30, 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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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 S

iOS 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 Klich

Android 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.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Brad T

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

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

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user