Skip to Content Go to accessibility page Keyboard shortcuts menu

2.7.5 Practice

Algebra 12.7.5 Practice

Search for key terms or text.

2.7.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

For questions 1 – 8, solve each system of equations to determine if there is one solution, no solution, or infinitely many solutions.

$\left\{\begin{array}{rcl}5x\;-\;3y\;&=&\;7\\x\;-\;0.6y\;&=&\;1.4\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}-x\;+\;2y\;&=&\;-1\\5x\;-\;10y\;&=&\;6\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}7x+6y&=&2\\-28x-24y&=&-8\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}-0.2x\;+\;0.4y\;&=&\;0.6\\x-2y&=&-3\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}-0.1x\;+\;0.2y\;&=&\;0.6\\5x-10y&=&1\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}3x+6y&=&11\\\;2x+4y&=&9\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}-x+2y=4\\\;2x-4y&=&1\end{array}\right.$

infinitely many solutions
no solution
one solution

$\left\{\begin{array}{rcl}3x-2y&=&5\\\;-9x+6y&=&-15\end{array}\right.$

infinitely many solutions
no solution
one solution

Which system of equations has infinitely many solutions?

$\left\{\begin{array}{l}-4x\;+\;3y\;=\;-12\\\;8x\;+\;6y\;=\;-24\end{array}\right.$
$\left\{\begin{array}{l}-4x\;+\;3y\;=\;12\\\;8x\;-\;6y\;=\;\;24\end{array}\right.$
$\left\{\begin{array}{l}4x\;+\;3y\;=\;12\\\;8x\;+\;6y\;=\;12\end{array}\right.$
$\left\{\begin{array}{l}4x\;+\;3y\;=\;12\\\;8x\;+\;6y\;=\;-24\end{array}\right.$

Which system of equations has no solution?

$\left\{\begin{array}{l}9x+21y=270\\\;3x+7y=90\end{array}\right.$
$\left\{\begin{array}{l}3x-7y=15\\\;3x+7y=40\end{array}\right.$
$\left\{\begin{array}{l}3x+7y=15\\\;6x+14y=30\end{array}\right.$
$\left\{\begin{array}{l}3x+7y=15\\\;3x+7y=40\end{array}\right.$

Order a print copy

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

Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/2-7-5-practice

© Aug 26, 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.