Unit Plan 18 (Grade 8 Math): Systems—Substitution & Elimination
8th graders master solving systems of linear equations using substitution and elimination, analyze special cases algebraically, and model real-world problems with systems, interpreting solutions clearly with units.
Focus: Solve systems algebraically; analyze special cases (no solution, infinitely many) and model with systems.
Grade Level: 8
Subject Area: Mathematics (Expressions & Equations • Functions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week moves from “see it on the graph” to solve it with algebra. Students practice substitution and elimination to find exact solutions to systems of two linear equations, including equations with rational coefficients. They choose a strategy, justify steps, and verify solutions. Special cases—no solution (parallel lines) and infinitely many solutions (same line)—are identified algebraically and connected back to graphs. The week culminates in modeling: writing and solving systems for real scenarios (break-even, mixtures, tickets, motion).
Essential Questions
- When is substitution the smarter choice, and when is elimination more efficient?
- How do algebraic steps reveal no solution or infinitely many solutions, and how does that connect to the graph?
- How do I turn a context into a system, solve it, and interpret the ordered-pair solution with units?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Solve systems of two linear equations by substitution (isolate, substitute, solve, back-substitute, check).
- Solve systems by elimination (align coefficients, add/subtract, scale when needed, solve, back-substitute, check).
- Classify special cases algebraically: contradiction (no solution) and identity (infinitely many solutions); tie to slopes/intercepts.
- Model real situations with systems (define variables, write equations, solve, and interpret with units and domain).
Standards Alignment — CCSS Grade 8
- 8.EE.8a: Understand solutions as points of intersection of the graphs.
- 8.EE.8b: Solve systems algebraically; solve simple cases by inspection; estimate solutions by graphing.
- 8.EE.8c: Solve real-world and mathematical problems leading to two linear equations in two variables.
Success Criteria (student-friendly)
- I can choose a method and explain why it fits the system.
- I can solve a system and verify by substituting the ordered pair in both equations.
- I can show, using algebra, why a system has no or infinitely many solutions.
- I can write a system from a story, solve it, and interpret the solution with units.