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

2.3.5 Practice

Algebra 12.3.5 Practice
Search for key terms or text.

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

1. Lin is solving this system of equations:

{ 6 x − 5 y = 34 3 x + 2 y = 8

She starts by rearranging the second equation to isolate the y variable: y = 4 − 1.5 x . She then substitutes the expression 4 − 1.5 x for y in the first equation, as shown:

6 x − 5 ( 4 − 1.5 x ) = 34
6 x − 20 − 7.5 x = 34

− 1.5 x = 54
x = − 36


y = 4 − 1.5 x

y = 4 − 1.5 ⋅ ( − 36 )

y = 58

Does Lin’s solution of ( − 36 , 58 ) makes both equations in the system true?

  1. No; Her solution does not make both equations true.
  2. yes; Her solution makes both equations true.
2. Which of the following is true of Lin’s solution?
  1. Lin’s solution of (-36, 58) is correct.
  2. Lin made an addition error. The correct answer is x = 0 and y = 4 , or (0,4).
  3. Lin made a multiplication error. The correct answer is x = 9 and y = 4 , or (9,4).
  4. Lin made a multiplication error. The correct answer is x = 4 and y = − 2 , or ( 4 , − 2 ) .

In 3 - 9, solve the systems of equations by substitution.


3. { 2 x + y = − 2 3 x − y = 7
  1. ( 2 , 6 )
  2. ( 1 , − 4 )
  3. ( 0 , − 2 )
  4. ( − 1 , 0 )

4. { x − 3 y = − 9 2 x + 5 y = 4

  1. ( − 3 , 2 )
  2. ( 0 , 3 )
  3. ( 2 , 0 )
  4. ( − 6 , 1 )

5. { − 2 x + 2 y = 6 2 y = − 6 x + 14

  1. ( − 3 , 0 )
  2. ( 2 , 1 )
  3. ( 0 , 7 )
  4. ( 1 , 4 )

6. { 3 x + 4 y = 1 y = − 2 5 x + 2

  1. ( − 5 , 4 )
  2. ( − 1 , 1 )
  3. ( 0 , 2 )
  4. ( 5 , 0 )

7. { 3 x + y = 10 x − 2 y = − 20

  1. ( 4 , 12 )
  2. ( − 4 , 8 )
  3. ( 0 , 10 )
  4. ( 2 , 2 )

8. { y = x − 6 y = − 3 2 x + 4

  1. ( 0 , 4 )
  2. ( 4 , − 2 )
  3. ( 2 , 1 )
  4. ( 6 , 0 )

9. { 2 x − 16 y = 8 − x − 8 y = − 4

  1. ( − 4 , − 1 )
  2. ( − 4 , 1 )
  3. ( 4 , 0 )
  4. ( 12 , 1 )

10. { y = − 2 3 x + 6 2 x − y = 2

  1. ( 6 , 2 )
  2. ( 3 , 4 )
  3. ( − 2 , 0 )
  4. ( 0 , 6 )

11. Tyler and Han are trying to solve this system by substitution:

{ x + 3 y = − 5 9 x + 3 y = 3

Tyler's first step is to isolate x in the first equation to get x = − 5 − 3 y .

Han's first step is to isolate 3y in the first equation to get 3 y = − 5 − x .

Solve using both methods to show that both first steps can be used to solve the system and will yield the same solution.

What is the solution to the system?

  1. ( − 5 , 0 )
  2. ( 4 , − 3 )
  3. ( 0 , 1 )
  4. ( 1 , − 2 )
PreviousNext
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.