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Math · Algebra 1 · Unit 2

Unit 2: Linear Equations and Systems

Students examine solving and graphing linear equations and systems of linear equations.

Worksheets

Every sheet has an answer key. Free to print, no login.

Unit
📝 Worksheet ✅ Answer guide
Concept
📝 Worksheet ✅ Answer key
Practice
Set 1
📝 Worksheet ✅ Answer key
Set 2
📝 Worksheet ✅ Answer key
Advanced
Set 1
📝 Worksheet ✅ Answer key
Set 2
📝 Worksheet ✅ Answer key

What this unit covers

A Writing and Modeling with Equations · 5 lessons
Goals
  • Interpret solutions to equations in one variable and in two variables.
  • Recognize that the graph of a linear equation in two variables represents all pairs of values that are solutions to the equation.
  • Write equations with numbers and variables to describe relationships and constraints.
Lessons
  1. Planning a Party
  2. Writing Equations to Model Relationships (Part 1) (Optional)
  3. Writing Equations to Model Relationships (Part 2)
  4. Equations and Their Solutions (Optional)
  5. Equations and Their Graphs (Optional)
B Manipulating Equations and Understanding Their Structure · 6 lessons
Goals
  • Determine the slope and vertical intercept of the graphs of linear equations by making use of structure or by rearranging the equations.
  • Rearrange multi-variable equations to highlight a particular quantity.
  • Recognize that “equivalent equations” are equations that have exactly the same solutions, and that multiple equivalent equations can represent the same relationship.
Lessons
  1. Equivalent Equations
  2. Explaining Steps for Rewriting Equations
  3. Which Variable to Solve for? (Part 1)
  4. Which Variable to Solve for? (Part 2)
  5. Connecting Equations to Graphs (Part 1)
  6. Connecting Equations to Graphs (Part 2)
C Systems of Linear Equations in Two Variables · 6 lessons
Goals
  • Determine whether a system of equations will have 0, 1, or infinitely many solutions by analyzing their structure or by graphing.
  • Use elimination or substitution to create one or more equivalent systems to help solve the original system.
Lessons
  1. Writing and Graphing Systems of Linear Equations
  2. Solving Systems by Substitution
  3. Solving Systems by Elimination (Part 1)
  4. Solving Systems by Elimination (Part 2)
  5. Solving Systems by Elimination (Part 3)
  6. Systems of Linear Equations and Their Solutions
D Let's Put It to Work · 2 lessons
Lessons
  1. Asking about Solving Systems (Optional)
  2. Linear Patterns (Optional)
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Adapted from the Illustrative Mathematics curriculum (v.360), licensed CC BY-NC 4.0. © Illustrative Mathematics.