Replace One Variable with an Equal Expression
Substitution uses one equation to express a variable, then replaces that variable in the other equation.
About 20 minutes, plus any extended practice
Open lesson 1Systems of Two Linear Equations
A system requires the same ordered pair to satisfy every equation. Substitution and elimination find that shared pair, while parallel or coincident line structure explains whether a system has none or many solutions.
Before you begin
- Solve linear equations; evaluate a formula; read an ordered pair.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Add Equations to Cancel a Variable
Elimination combines equations so one variable’s coefficients sum to zero.
About 20 minutes, plus any extended practice
Open lesson 2Recognize Parallel Distinct Lines
Lines with equal slopes and different intercepts never meet in the coordinate plane.
About 20 minutes, plus any extended practice
Open lesson 3Use Two Constraints to Recover Two Counts
A total count and a weighted total can become two equations.
About 20 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- California CCSS mathematics topic reference: topic reference — Systems of Two Linear Equations
These references informed the topic selection. They do not certify complete standards alignment.