Simultaneous equations might sound intimidating, but they're just two equations... Show more
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Updated Mar 29, 2026
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Understanding Simultaneous Equations
robyn๐๐ค
@rqbny
1 / 5
Getting Started with Simultaneous Equations
When you see two equations with the same variables, you're dealing with simultaneous equations. The goal is to find the values of both x and y that make both equations true at the same time.
Your first step is always to label your equations - this keeps you organised and prevents silly mistakes. Simply write โ next to the first equation and โก next to the second one.
Quick Tip: Always label your equations from the start - it'll save you loads of confusion later!
Making the Coefficients Match
Now you need to make one of the variables have the same coefficient in both equations. Look at the numbers in front of y (or x) and find their lowest common multiple.
In this example, 3 and 2 both go into 6. Multiply the first equation by 2 to get -6y, and multiply the second equation by 3 to get +6y. Remember to multiply the entire equation, not just the y term!
This gives you two new equations with matching y coefficients. Label these as equations โข and โฃ to stay organised.
Remember: Whatever you do to one side of an equation, you must do to the other side too!
Eliminating Variables
Here's where the magic happens! Look at the signs in front of your matching coefficients. If they're opposite signs (one positive, one negative), you add the equations together. If they're the same signs, you subtract.
Since -6y and +6y are opposites, add the equations. The y terms cancel out completely, leaving you with just x terms. Solve this simple equation to find your x value.
In this case, 17x = -34, so x = -2. You've successfully found half the answer!
Key Point: Opposite signs mean add, same signs mean subtract - this always eliminates one variable!
Finding the Second Variable
Time for substitution! Take your x value and plug it back into either of your original equations - pick whichever looks easier to work with.
Replace x with -2 in the equation 5x + 2y = 4. This becomes 5(-2) + 2y = 4, which simplifies to -10 + 2y = 4. Rearrange to get 2y = 14, so y = 7.
You now have both values: x = -2 and y = 7. But don't celebrate just yet - there's one crucial step left!
Pro Tip: Choose the simpler-looking original equation for substitution - it'll make your calculations much easier!
Checking Your Answer
Never skip the checking step - it catches any calculation errors and confirms you've got the right answer. Use the same equation you picked for substitution.
Substitute both x = -2 and y = 7 into 5x + 2y = 4. Work it out: 5(-2) + 2(7) = -10 + 14 = 4. Perfect! This matches the right-hand side of your equation.
If your check doesn't work out, go back through your steps to find where you made an error. Getting into this habit will boost your confidence and improve your marks.
Final Check: Your substituted values should make the original equation true - if they don't, retrace your steps!
We thought youโd 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 โ all at your fingertips.
Most popular content in Maths
maths helpbook to get grade 9
material from online, not my personal advice
Maths9
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Can't find what you're looking for? Explore other subjects.
Students love us โ and so will you.
4.6/5
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4.7/5
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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
Understanding Simultaneous Equations
robyn๐๐ค
@rqbny
Simultaneous equations might sound intimidating, but they're just two equations working together to find the values of x and y. Once you learn the step-by-step method, you'll be solving these confidently in no time!
Getting Started with Simultaneous Equations
When you see two equations with the same variables, you're dealing with simultaneous equations. The goal is to find the values of both x and y that make both equations true at the same time.
Your first step is always to label your equations - this keeps you organised and prevents silly mistakes. Simply write โ next to the first equation and โก next to the second one.
Quick Tip: Always label your equations from the start - it'll save you loads of confusion later!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Making the Coefficients Match
Now you need to make one of the variables have the same coefficient in both equations. Look at the numbers in front of y (or x) and find their lowest common multiple.
In this example, 3 and 2 both go into 6. Multiply the first equation by 2 to get -6y, and multiply the second equation by 3 to get +6y. Remember to multiply the entire equation, not just the y term!
This gives you two new equations with matching y coefficients. Label these as equations โข and โฃ to stay organised.
Remember: Whatever you do to one side of an equation, you must do to the other side too!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Eliminating Variables
Here's where the magic happens! Look at the signs in front of your matching coefficients. If they're opposite signs (one positive, one negative), you add the equations together. If they're the same signs, you subtract.
Since -6y and +6y are opposites, add the equations. The y terms cancel out completely, leaving you with just x terms. Solve this simple equation to find your x value.
In this case, 17x = -34, so x = -2. You've successfully found half the answer!
Key Point: Opposite signs mean add, same signs mean subtract - this always eliminates one variable!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Finding the Second Variable
Time for substitution! Take your x value and plug it back into either of your original equations - pick whichever looks easier to work with.
Replace x with -2 in the equation 5x + 2y = 4. This becomes 5(-2) + 2y = 4, which simplifies to -10 + 2y = 4. Rearrange to get 2y = 14, so y = 7.
You now have both values: x = -2 and y = 7. But don't celebrate just yet - there's one crucial step left!
Pro Tip: Choose the simpler-looking original equation for substitution - it'll make your calculations much easier!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Checking Your Answer
Never skip the checking step - it catches any calculation errors and confirms you've got the right answer. Use the same equation you picked for substitution.
Substitute both x = -2 and y = 7 into 5x + 2y = 4. Work it out: 5(-2) + 2(7) = -10 + 14 = 4. Perfect! This matches the right-hand side of your equation.
If your check doesn't work out, go back through your steps to find where you made an error. Getting into this habit will boost your confidence and improve your marks.
Final Check: Your substituted values should make the original equation true - if they don't, retrace your steps!
We thought youโd 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 โ all at your fingertips.
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Most popular content in Maths
maths helpbook to get grade 9
material from online, not my personal advice
Maths9
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us โ and so will you.
4.6/5
App Store
4.7/5
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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