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Hannah Murdoch
01/09/2025
Maths
Simultaneous Equations Examples - National 5 Maths
Practice Problems and Advanced Techniques
This page builds upon the previous concepts by presenting more complex simultaneous equations and their solutions. It also introduces practice problems to reinforce learning.
The page starts with a set of equations: 3x + 2y = 17 2x + 5y = 4
It demonstrates the solution process using the elimination method:
- Multiply the first equation by 5 and the second by 2
- Subtract the resulting equations to eliminate y
- Solve for x
- Substitute x back into one of the original equations to solve for y
Example: 15x + 10y = 85 4x + 10y = 8 Subtracting these equations eliminates y: 11x = 77 x = 7
The page then provides practice problems for students to solve:
1a) 7b + 3g = 136 2b + 2g = 86
1b) 5b + 4g = 215 15b + 12g = 645
Highlight: These practice problems are designed to help students apply the techniques for balancing equations in math that they've learned.
The solutions to these problems are also provided, showing the step-by-step process for each. This reinforces the importance of methodical problem-solving in algebra.
Definition: Elimination method - A technique for solving simultaneous equations by adding or subtracting equations to remove one variable, allowing for the solution of the remaining variable.
The page concludes with more complex equations, encouraging students to apply their knowledge to increasingly challenging problems:
- 4x + 5y = -3 6x - 2y = 25
This final example demonstrates how to handle equations with negative numbers and fractions, further expanding students' understanding of solving simultaneous equations step by step.
Solving Simultaneous Equations
This page introduces the concept of simultaneous equations and demonstrates various solving methods. It provides a detailed walkthrough of solving different types of equations, emphasizing the step-by-step approach.
The page begins with a set of simultaneous equations: 3y + 2x = 12 3x = 5
It then proceeds to show the solution process, which involves manipulating the equations to isolate variables. The method demonstrated here is the substitution method, where one equation is rearranged to express one variable in terms of the other.
Example: 3x = 5 x = 5/3
This value of x is then substituted into the other equation: 3y + 2 = 12
The solution continues by solving for y: 3y = 12 - 10/3 3y = 26/3 y = 26/9
The page also includes other examples of simultaneous equations with different complexities: 15y + 6x = 36 8y - 6x = 10
These equations are solved using the elimination method, where equations are added or subtracted to eliminate one variable.
Highlight: The page emphasizes the importance of showing all steps clearly, which is crucial for understanding complex algebraic expressions.
Vocabulary: Simultaneous equations - A set of equations involving the same variables that must be solved together to find values that satisfy all equations simultaneously.
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4.9/5
App Store
4.8/5
Google 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 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
Best app on earth! no words because it’s too good
Thomas R
iOS user
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.
Basil
Android user
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.
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
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
Android user
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
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 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
Paul T
iOS user
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
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.
Basil
Android user
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.
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
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
Android user
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
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 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
Paul T
iOS user
Easy Steps for Solving Equations and Algebra
A comprehensive guide to solving simultaneous equations step by step and understanding complex algebraic expressions. This resource covers various methods and techniques for balancing equations in math, providing clear examples and explanations for students.
- Introduces the concept of... Show more
Practice Problems and Advanced Techniques
This page builds upon the previous concepts by presenting more complex simultaneous equations and their solutions. It also introduces practice problems to reinforce learning.
The page starts with a set of equations: 3x + 2y = 17 2x + 5y = 4
It demonstrates the solution process using the elimination method:
- Multiply the first equation by 5 and the second by 2
- Subtract the resulting equations to eliminate y
- Solve for x
- Substitute x back into one of the original equations to solve for y
Example: 15x + 10y = 85 4x + 10y = 8 Subtracting these equations eliminates y: 11x = 77 x = 7
The page then provides practice problems for students to solve:
1a) 7b + 3g = 136 2b + 2g = 86
1b) 5b + 4g = 215 15b + 12g = 645
Highlight: These practice problems are designed to help students apply the techniques for balancing equations in math that they've learned.
The solutions to these problems are also provided, showing the step-by-step process for each. This reinforces the importance of methodical problem-solving in algebra.
Definition: Elimination method - A technique for solving simultaneous equations by adding or subtracting equations to remove one variable, allowing for the solution of the remaining variable.
The page concludes with more complex equations, encouraging students to apply their knowledge to increasingly challenging problems:
- 4x + 5y = -3 6x - 2y = 25
This final example demonstrates how to handle equations with negative numbers and fractions, further expanding students' understanding of solving 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
Solving Simultaneous Equations
This page introduces the concept of simultaneous equations and demonstrates various solving methods. It provides a detailed walkthrough of solving different types of equations, emphasizing the step-by-step approach.
The page begins with a set of simultaneous equations: 3y + 2x = 12 3x = 5
It then proceeds to show the solution process, which involves manipulating the equations to isolate variables. The method demonstrated here is the substitution method, where one equation is rearranged to express one variable in terms of the other.
Example: 3x = 5 x = 5/3
This value of x is then substituted into the other equation: 3y + 2 = 12
The solution continues by solving for y: 3y = 12 - 10/3 3y = 26/3 y = 26/9
The page also includes other examples of simultaneous equations with different complexities: 15y + 6x = 36 8y - 6x = 10
These equations are solved using the elimination method, where equations are added or subtracted to eliminate one variable.
Highlight: The page emphasizes the importance of showing all steps clearly, which is crucial for understanding complex algebraic expressions.
Vocabulary: Simultaneous equations - A set of equations involving the same variables that must be solved together to find values that satisfy all equations simultaneously.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and 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.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google 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 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
Best app on earth! no words because it’s too good
Thomas R
iOS user
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.
Basil
Android user
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.
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
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
Android user
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
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 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
Paul T
iOS user
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
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.
Basil
Android user
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.
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
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
Android user
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
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 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
Paul T
iOS user