Linear Systems - Unit 3 Bundle - Texas Algebra 2 Curriculum

Grade Levels
10th - 12th
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161 pages + keys
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  1. Get a complete, ready-to-print curriculum covering topics from the Algebra 2 TEKS.This curriculum bundle contains guided notes handouts, practice worksheets, exit tickets, warm-ups, reviews, mid-unit assessments, tests, and concept organizers - all aligned to the Texas Algebra 2 state standards (TEK
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Get a complete, ready-to-print unit covering topics from the Algebra 2 TEKS including 3-variable systems of equations and systems of linear inequalities.

Substitution, elimination, Gaussian elimination, inverse matrices, augmented matrices, and linear programming are among the topics included in this unit.


The study of linear systems in Algebra 2 extends students' prior knowledge about writing and solving two-variable systems of equations and expands on those foundational concepts to introduce writing and solving 3-variable systems of linear equations.

Students will solve 3x3 systems of linear equations using substitution, elimination, Gaussian elimination, inverse matrices, and augmented matrices. Teachers may opt to teach only the methods that are best suited to their students and course.

Students also will formulate and graph systems of linear inequalities, including applying their knowledge of linear inequalities to linear programming situations.

These no-prep resources include 8 lessons with guided notes, an exit ticket, a next-day warm-up, and 2 extra practice assignments per lesson.  The unit also includes mid-unit and end-of-unit reviews, mid-unit and end-of-unit editable assessments, and concept organizers. Increase student engagement with 10 TEKS-aligned activities! Increase student engagement with 10 TEKS-aligned activities!


TEACHERS LOVE the worked-out keys included with the lessons notes. Feel confident delivering instruction on these sometimes tricky topics! It is a major time-saver if you don’t have quite enough time to create your own guided notes key for the day.

STUDENTS LOVE the reduced note-taking burden with the guided notes handouts. Fill-in-the-blank vocabulary improves the accuracy of students’ notes and frees up more time for showing mathematical steps. 

TEACHERS LOVE the multiple versions of each practice worksheet, review, and assessment and they take full advantage of the EDITABLE versions of the mid-unit assessment form and unit test.

STUDENTS LOVE the complementary concept organizers that help them organize concepts and procedures.  

TEACHERS LOVE the pre-made exit tickets and next-day warm-ups that support skills from every lesson in the unit. Print 4-per-page or project on the board and record answers on scratch paper.

STUDENTS LOVE the variety of fun and engaging activities!  


Most resources are in non-editable PDF format.

  • Editable versions of the mid-unit assessment and test are also included in .docx format for MS Word.
  • 5 digital activities compatible with Google Slides and Google Classroom™ are included. (Printable versions of the digital activities are included in PDF format.)
  • 5 paper-based activities in PDF format are included.


Lesson 0: 2x2 Review (Free Bonus Lesson!)

Students will:

  • solve 2-variable systems of linear equations algebraically
  • review substitution and elimination methods

Lesson 1: 3x3 Substitution

Students will:

  • solve three-variable systems of linear equations algebraically using substitution
  • solve systems resulting in no solution and infinitely many solutions

Lesson 2: 3x3 Applications

Students will:

  • formulate three-variable systems of linear equations from word problems
  • solve systems and interpret the meaning of the solutions within the context of the applied situations

Lesson 3: 3x3 Elimination

Students will:

  • solve three-variable systems of linear equations algebraically using elimination (combination)
  • solve systems resulting in no solution and infinitely many solutions

Lesson 4: Gaussian Elimination

Students will:

  • use Gaussian elimination to solve three-variable systems of linear equations
  • organize systems as augmented matrices
  • use row operations to transform the matrix into a system that can be solved easily using substitution

Lesson 5: Inverse Matrices

Students will:

  • solve three-variable systems of linear equations using inverse matrices and technology
  • write matrix equations
  • compute X=A^(-1) B to calculate the solutions to systems of equations

Lesson 6: Augmented Matrices

Students will:

  • solve three-variable systems of linear equations using technology with matrices
  • rewrite systems of equations augmented matrices
  • solve three-variable systems using the reduced row echelon form command, rref ()
  • interpret the solution

Lesson 7: Systems of Linear Inequalities

Students will:

  • graph and write systems of linear inequalities

Lesson 8: Linear Programming

Students will:

  • formulate and graph systems of two or more linear inequalities from problem situations
  • write constraints and objective functions for linear programming situations
  • evaluate objective function at the vertices of the region bounded by the constraints to maximize or minimize the objective function


  • The Lesson Notes are designed for use as a note-taking guide combined with guided practice.
  • Practice A and Practice B are suitable for use as in-class practice and homework. Two comparable forms are included for increased versatility.
  • The Exit Ticket is designed for a quick concept check at the end of the class period.
  • The Warm-Up is designed for next-day use to reinforce the previous day’s learning.
  • One-page display versions of the exit ticket and warm-up are included. Display the PDF page on a screen for student viewing and have students record their responses on notebook paper or scratch paper to save on printing.


  • 5 Concept Organizers offer complimentary alternatives for note-taking or post-lesson concept reinforcement.
  • The Mid-Unit Review (Forms A and B) provides an opportunity for students to practice the concepts they learned in the first part of the unit.
  • The Mid-Unit Assessment (Forms A and B) may be used as a test, quiz, or daily assignment to meet the specific needs of your students. Editable versions of Forms A and B are included as a .docx file for MS Word.
  • The Unit Review (Forms A and B) helps students focus on the key concepts studied throughout the unit.
  • The Unit Test (Forms A, B, and C) comes in two comparable multiple-choice forms (A and B) and one free-response form (C). The test key includes TEKS alignment for each question to facilitate easy data analysis. Editable versions of Forms A and B are included as a .docx file for MS Word.



3x3 Systems of Equations Task Card Activity

3x3 Systems of Linear Equations Scavenger Hunt

Matrix Relay Activity

Systems of Linear Inequalities Riddle

Linear Programming Poster Activity Guide


(Each digital activity also includes a printable version.)

3x3 Systems by Substitution Activity for Google Slides™

3x3 Systems of Equations Word Problems for Google Slides™

3x3 Linear Systems Unscramble Activity for Google Slides™

Systems of Inequalities Activity for Google Slides™

Formulating Systems of Linear Inequalities for Google Slides™

Please view the previews in the bundle section for more detail.


This unit and activity bundle is perfect for providing a complete TEKS-aligned unit or for supplementing existing resources. Use every resource or pick-and-choose from the many options to meet the needs of your students!


⭐️⭐️⭐️⭐️⭐️ “Great job creating a resource over linear systems and matrices. Organized very well with teaching solving by hand and then the calculator. [...]”


Supports Algebra 2 Texas Essential Knowledge and Skills (TEKS)

Standards: 2A.3A, 2A.3B, 2A.3E, 2A.3F, 2A.3G, (A.5C Algebra 1 review)

A note from Allison at Math Beach Solutions about standards alignment: This resource was designed from the ground up to provide ready-made resources for Texas teachers to implement to facilitate their students’ mastery of the Algebra 2 TEKS (Texas Essential Knowledge and Skills TAC §111.40). A considerable effort has been made to ensure the TEKS are addressed thoroughly, but these resources will reflect my understanding of the TEKS. As always, continue to use your professional judgment and experience when lesson planning.


⭐️ Bundle & save for a discount ⭐️

Purchase the Texas Algebra 2 Curriculum to get all 12 units and activities. The curriculum lasts the entire year. It also includes an editable mid-term and editable final exam!

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Looking for a long-term homework solution? Check out Algebra 2 Skill Spirals Review Workbook for a year-long solution for homework, warm-ups, or tutorial session resources. It supports the Texas Algebra 2 TEKS, too!


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Permission to copy for single classroom use only. 

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Total Pages
161 pages + keys
Answer Key
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