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May 23, 2023

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Fun with Math: Solving Linear Systems Using Substitution & Elimination

K

katharine

@katharinemae27

This transcript covers solving linear systems using substitution and elimination... Show more

Step 1 (chapter 5 Solving 2-variable linear systems by SUBSTITUTION apter S *Step 1-solve 1 equation for other variable *Step 2- Substitute

Solving Linear Systems by Elimination

This page focuses on the elimination method in algebra for solving systems of linear equations, providing a step-by-step guide and examples.

The elimination method consists of four main steps:

  1. Multiply one or both equations to create opposite coefficients for one variable
  2. Add the equations to eliminate one variable
  3. Solve for the remaining variable
  4. Substitute the value found in step 3 into either original equation to solve for the other variable

Highlight: The elimination method is particularly effective when coefficients can be easily manipulated to cancel out a variable.

Three examples demonstrate the application of the elimination method:

Example 1 solves: 4x + 5y = 3 -3x + 2y = 38

Example 2 addresses: 5x - 3y = 35 8x + 2y = 22

Example 3 presents a word problem about purchasing throw blankets with embroidered letters, showing how to apply the elimination method to practical situations.

Example: In the throw blanket problem, students learn to set up equations based on given information: x + 6y = 29 and x + 3y = 24.50, where x represents the cost of the blanket and y represents the cost per letter.

Vocabulary: Elimination method - A technique for solving systems of equations by adding or subtracting equations to cancel out one variable.

The page concludes with the solution to the word problem, demonstrating how to interpret the mathematical results in the context of the original question about blanket and embroidery costs.

Step 1 (chapter 5 Solving 2-variable linear systems by SUBSTITUTION apter S *Step 1-solve 1 equation for other variable *Step 2- Substitute

Solving Linear Systems by Substitution

This page introduces the substitution method for solving linear systems and provides detailed examples to illustrate the process.

The substitution method involves three key steps:

  1. Solve one equation for one variable
  2. Substitute the expression into the other equation and solve for the remaining variable
  3. Use the value found in step 2 to solve for the final variable

Highlight: The substitution method is particularly useful when one equation is already solved for a variable or can be easily rearranged.

Three examples are provided to demonstrate the application of the substitution method:

Example 1 solves the system: x + y = 3 3x + y = -1

Example 2 tackles: x - y = -4 2x + y = 4

Example 3 presents a word problem involving ticket sales at a comedy club, demonstrating how to apply the substitution method to real-world scenarios.

Example: In the comedy club problem, students learn to set up equations based on given information: 68x + 136y = 1088 and 79x + 140y = 1183, where x represents adult ticket price and y represents student ticket price.

Vocabulary: Linear system - A set of two or more linear equations with the same variables.

The page concludes with the solution to the word problem, illustrating how to interpret the mathematical results in the context of the original question.



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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

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

Subjects

Arithmetic

 

Arithmetic

•

58

•

May 23, 2023

•

2 pages

Fun with Math: Solving Linear Systems Using Substitution & Elimination

K

katharine

@katharinemae27

This transcript covers solving linear systems using substitution and elimination methods. It provides step-by-step instructions and examples for both techniques, including word problems.

Overall Summary:

The document explains two methods for solving systems of linear equations:

  • Solving linear systems by... Show more

Step 1 (chapter 5 Solving 2-variable linear systems by SUBSTITUTION apter S *Step 1-solve 1 equation for other variable *Step 2- Substitute

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 Linear Systems by Elimination

This page focuses on the elimination method in algebra for solving systems of linear equations, providing a step-by-step guide and examples.

The elimination method consists of four main steps:

  1. Multiply one or both equations to create opposite coefficients for one variable
  2. Add the equations to eliminate one variable
  3. Solve for the remaining variable
  4. Substitute the value found in step 3 into either original equation to solve for the other variable

Highlight: The elimination method is particularly effective when coefficients can be easily manipulated to cancel out a variable.

Three examples demonstrate the application of the elimination method:

Example 1 solves: 4x + 5y = 3 -3x + 2y = 38

Example 2 addresses: 5x - 3y = 35 8x + 2y = 22

Example 3 presents a word problem about purchasing throw blankets with embroidered letters, showing how to apply the elimination method to practical situations.

Example: In the throw blanket problem, students learn to set up equations based on given information: x + 6y = 29 and x + 3y = 24.50, where x represents the cost of the blanket and y represents the cost per letter.

Vocabulary: Elimination method - A technique for solving systems of equations by adding or subtracting equations to cancel out one variable.

The page concludes with the solution to the word problem, demonstrating how to interpret the mathematical results in the context of the original question about blanket and embroidery costs.

Step 1 (chapter 5 Solving 2-variable linear systems by SUBSTITUTION apter S *Step 1-solve 1 equation for other variable *Step 2- Substitute

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 Linear Systems by Substitution

This page introduces the substitution method for solving linear systems and provides detailed examples to illustrate the process.

The substitution method involves three key steps:

  1. Solve one equation for one variable
  2. Substitute the expression into the other equation and solve for the remaining variable
  3. Use the value found in step 2 to solve for the final variable

Highlight: The substitution method is particularly useful when one equation is already solved for a variable or can be easily rearranged.

Three examples are provided to demonstrate the application of the substitution method:

Example 1 solves the system: x + y = 3 3x + y = -1

Example 2 tackles: x - y = -4 2x + y = 4

Example 3 presents a word problem involving ticket sales at a comedy club, demonstrating how to apply the substitution method to real-world scenarios.

Example: In the comedy club problem, students learn to set up equations based on given information: 68x + 136y = 1088 and 79x + 140y = 1183, where x represents adult ticket price and y represents student ticket price.

Vocabulary: Linear system - A set of two or more linear equations with the same variables.

The page concludes with the solution to the word problem, illustrating how to interpret the mathematical results in the context of the original question.

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

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