Lesson objective: Apply knowledge of systems to solve a simple system with multiple variables and constraints.

This lesson provides an opportunity for students to apply their knowledge and understanding of two-variable systems to a real-life situation. Students are asked to solve multiple relationships to determine the running time of four runners, and then use this information to determine how they would place in a staggered-start 100 meter race.

Key Concept students will use:

- We can write and solve systems of linear equations in two variables to solve problems with multiple simultaneous constraints.

Skills students will use:

- Solve a simple system by substitution or by other algebraic methods. (Grade 8, Unit 11)
- Determine the unit rates and write a slope-intercept equation. (Grade 8, Unit 7)
- Use graphs or tables to find connections between multiple linear relationships. (Grade 8, Unit 7)

Students engage in Mathematical Practice 4 (Model with mathematics) as they solve multiple equations to determine individual running times. They then use tables, graphs, or equations to determine which runners would pass each other in a staggered race.

**Key vocabulary: **

- system of equations
- unit rate
- substitution