Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

2.7.1 Systems of Linear Equations with Infinitely Many Solutions

Algebra 12.7.1 Systems of Linear Equations with Infinitely Many Solutions

Search for key terms or text.

Warm Up

Andre is trying to solve this system of equations:

{x+y=34x=124y{x+y=34x=124y

Looking at the first equation, he thought, “The solution to the system is a pair of numbers that add up to 3. I wonder which two numbers they are.”

1.

Choose any two numbers that add up to 3. Let the first one be the xx-value and the second one be the yy-value.

2.

The pair of values you chose is a solution to the first equation. Check if it is also a solution to the second equation. Then, pause for a brief discussion with your group.

3.

How many solutions does the system have? Use what you know about equations and solving systems to show that you are right.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.