The Value Swap: Solving Systems by Substitution
Shared by A STEM Educator
Students will solve systems of two linear equations using substitution by isolating a variable, substituting an equivalent expression, solving the resulting single-variable equation, and interpreting special-case results (infinite solutions, no solution).
Lesson Overview
Students progress from a real-world burger-and-drink riddle to pure symbolic substitution, discovering that replacing one variable's expression into another equation collapses two unknowns into one solvable equation. The lesson uses BTC pedagogy with VNPS, random groups, and thin-sliced tasks.
Materials
- Vertical whiteboards or large chart paper
- Dry-erase markers (one per group)
- Erasers or paper towels
- Random grouping cards or app (e.g., Flippity)
- Desmos Classroom activity (teacher-prepared)
- Exit slip half-sheets
Scaffolded Task Progression
A restaurant menu features a special combo deal: a burger and a drink together cost $12. The menu also notes that a burger costs exactly the same as three drinks. How much does a single drink cost? How much does a single burger cost? Show your logic clearly on your board using drawings or symbols.
Now translate your burger-and-drink solution into a formal system using variables (burger price) and (drink price).
Write both equations. Then solve the system using substitution. On your board, circle the exact spot where you replaced the burger variable with an expression involving .
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