Subjects
Biology
Chemistry
AP Chemistry
English
AP English Literature
Algebra 1
Dec 3, 2025
63
11 pages
intellect @intellect
The elimination method is a powerful technique for solving systems of equations that makes one variable disappear completely.... Show more
Ever wish you could just make one variable vanish when solving two equations at once? That's exactly what the elimination method does! This technique works by creating opposite coefficients for one variable, so when you add the equations together, that variable cancels out completely.
The beauty of elimination is that sometimes the opposite coefficients are already there waiting for you. Other times, you'll need to multiply one or both equations by a strategic number to create them.
Quick Tip Look for the variable that's easiest to eliminate first - it'll save you time and reduce mistakes!
The elimination method follows four straightforward steps that you can master with practice. Step 1 requires both equations in standard form . Step 2 involves multiplying equations to create opposite coefficients for one variable.
Step 3 is where the magic happens - you add the equations together and watch one variable disappear! The remaining equation has just one variable, making it easy to solve.
Step 4 wraps everything up by substituting your answer back into either original equation to find the other variable. This systematic approach works every single time.
Remember Always check your final answer by plugging both values into both original equations!
Let's tackle a real problem -4x - 6y = -12 and -x + 12y = -30. Both equations are already in standard form, so we skip to creating opposite coefficients.
To eliminate y, multiply the first equation by 2, giving us -8x - 12y = -24. Now the y-terms will cancel perfectly when we add the equations together.
Adding gives us -9x = -54, so x = 6. Substitute x = 6 into either original equation -4(6) - 6y = -12 becomes y = -2. Final answer (6, -2)
Strategy Tip Choose to eliminate the variable that requires the smallest multipliers - it keeps your numbers manageable!
Here's a trickier one 10x - 4y = 22 and -3y = -1 - 4x. First, rewrite the second equation in standard form 4x - 3y = -1.
To eliminate y, we need opposite coefficients for the y-terms. Multiply the first equation by 3 and the second by -4. This gives us 30x - 12y = 66 and -16x + 12y = 4.
Adding these new equations 14x = 70, so x = 5. Substitute back 10(5) - 4y = 22 leads to y = 7. Final answer (5, 7)
Pro Move When both equations need multiplying, pick numbers that create the least complicated arithmetic!
Word problems become manageable when you translate them into elimination problems. A music store sold 27 trumpets and clarinets total, with trumpets at 99, earning $3,223 total.
Set up your equations t + c = 27 (total instruments) and 149t + 99c = 3,223 (total sales). To eliminate c, multiply the first equation by -99.
This gives -99t - 99c = -2,673. Adding to the second equation 50t = 550, so t = 11 trumpets. Therefore, c = 16 clarinets.
Word Problem Hack Always define your variables clearly and double-check that your equations match the problem's constraints!
Sometimes elimination reveals that your system has no solution or infinitely many solutions. These special cases happen when both variables cancel out during the elimination process.
If you end up with a false statement like 0 = 5, your system has no solution - the lines are parallel and never intersect. If you get a true statement like 0 = 0, you have infinitely many solutions - the equations represent the same line.
Don't panic when this happens! These special cases are just as valid as regular solutions, and recognizing them shows you understand systems of equations deeply.
Watch Out Special cases often appear on tests, so practice identifying when both variables disappear!
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
6
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
App Store
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
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
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
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
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
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
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
intellect
@intellect
The elimination method is a powerful technique for solving systems of equations that makes one variable disappear completely. Instead of struggling with substitution, you'll create opposite coefficients and add equations together to eliminate variables systematically.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Ever wish you could just make one variable vanish when solving two equations at once? That's exactly what the elimination method does! This technique works by creating opposite coefficients for one variable, so when you add the equations together, that variable cancels out completely.
The beauty of elimination is that sometimes the opposite coefficients are already there waiting for you. Other times, you'll need to multiply one or both equations by a strategic number to create them.
Quick Tip: Look for the variable that's easiest to eliminate first - it'll save you time and reduce mistakes!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The elimination method follows four straightforward steps that you can master with practice. Step 1 requires both equations in standard form . Step 2 involves multiplying equations to create opposite coefficients for one variable.
Step 3 is where the magic happens - you add the equations together and watch one variable disappear! The remaining equation has just one variable, making it easy to solve.
Step 4 wraps everything up by substituting your answer back into either original equation to find the other variable. This systematic approach works every single time.
Remember: Always check your final answer by plugging both values into both original equations!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Let's tackle a real problem: -4x - 6y = -12 and -x + 12y = -30. Both equations are already in standard form, so we skip to creating opposite coefficients.
To eliminate y, multiply the first equation by 2, giving us -8x - 12y = -24. Now the y-terms will cancel perfectly when we add the equations together.
Adding gives us -9x = -54, so x = 6. Substitute x = 6 into either original equation: -4(6) - 6y = -12 becomes y = -2. Final answer: (6, -2)
Strategy Tip: Choose to eliminate the variable that requires the smallest multipliers - it keeps your numbers manageable!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Here's a trickier one: 10x - 4y = 22 and -3y = -1 - 4x. First, rewrite the second equation in standard form: 4x - 3y = -1.
To eliminate y, we need opposite coefficients for the y-terms. Multiply the first equation by 3 and the second by -4. This gives us 30x - 12y = 66 and -16x + 12y = 4.
Adding these new equations: 14x = 70, so x = 5. Substitute back: 10(5) - 4y = 22 leads to y = 7. Final answer: (5, 7)
Pro Move: When both equations need multiplying, pick numbers that create the least complicated arithmetic!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Word problems become manageable when you translate them into elimination problems. A music store sold 27 trumpets and clarinets total, with trumpets at 99, earning $3,223 total.
Set up your equations: t + c = 27 (total instruments) and 149t + 99c = 3,223 (total sales). To eliminate c, multiply the first equation by -99.
This gives -99t - 99c = -2,673. Adding to the second equation: 50t = 550, so t = 11 trumpets. Therefore, c = 16 clarinets.
Word Problem Hack: Always define your variables clearly and double-check that your equations match the problem's constraints!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Sometimes elimination reveals that your system has no solution or infinitely many solutions. These special cases happen when both variables cancel out during the elimination process.
If you end up with a false statement like 0 = 5, your system has no solution - the lines are parallel and never intersect. If you get a true statement like 0 = 0, you have infinitely many solutions - the equations represent the same line.
Don't panic when this happens! These special cases are just as valid as regular solutions, and recognizing them shows you understand systems of equations deeply.
Watch Out: Special cases often appear on tests, so practice identifying when both variables disappear!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
6
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
App Store
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
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
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
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
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
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
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
Math 8th Grade
Pre-Calculus
Calculus 1