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Unit 2: Linear Equations and Systems
Students examine solving and graphing linear equations and systems of linear equations.
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Unit
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Concept
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Practice
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Advanced
Try more challenging problems.
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
- Planning a Party
- Writing Equations to Model Relationships (Part 1) (Optional)
- Writing Equations to Model Relationships (Part 2)
- Equations and Their Solutions (Optional)
- 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
- Equivalent Equations
- Explaining Steps for Rewriting Equations
- Which Variable to Solve for? (Part 1)
- Which Variable to Solve for? (Part 2)
- Connecting Equations to Graphs (Part 1)
- 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
- Writing and Graphing Systems of Linear Equations
- Solving Systems by Substitution
- Solving Systems by Elimination (Part 1)
- Solving Systems by Elimination (Part 2)
- Solving Systems by Elimination (Part 3)
- Systems of Linear Equations and Their Solutions
D Let's Put It to Work · 2 lessons
Lessons
- Asking about Solving Systems (Optional)
- Linear Patterns (Optional)
Adapted from the Illustrative Mathematics curriculum (v.360), licensed CC BY-NC 4.0. © Illustrative Mathematics.