Lesson 15
Writing Systems of Equations
Lesson Narrative
Previously, students have been given systems of equations to interpret and solve. In this lesson, they learn to write their own systems representing different contexts, and to interpret the solutions for those systems. Different contexts can lead to systems in different forms, so students also continue to practice looking at different systems and thinking ahead about how to solve them. When students represent a realworld problem with a system, they develop an important skill for mathematical modeling (MP4).
Learning Goals
Teacher Facing
 Categorize (in writing) systems of equations, including systems with infinitely many or no solutions, and calculate the solution for a system using a variety of strategies.
 Create a system of equations that represents a situation and interpret (orally and in writing) the solution in context.
Student Facing
Let’s write systems of equations from realworld situations.
Required Materials
Required Preparation
You will need the Info Gap: Racing and Play Tickets blackline master for this lesson. Make 1 copy for every 4 students, and cut them up ahead of time.
Learning Targets
Student Facing
 I can write a system of equations from a realworld situation.
CCSS Standards
Glossary Entries

system of equations
A system of equations is a set of two or more equations. Each equation contains two or more variables. We want to find values for the variables that make all the equations true.
These equations make up a system of equations:
\(\displaystyle \begin{cases} x + y = \text2\\x  y = 12\end{cases}\)
The solution to this system is \(x=5\) and \(y=\text7\) because when these values are substituted for \(x\) and \(y\), each equation is true: \(5+(\text7)=\text2\) and \(5(\text7)=12\).
Print Formatted Materials
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Additional Resources
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