# 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 real-world 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 real-world situations.

### 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.

### Student Facing

• I can write a system of equations from a real-world situation.

Building Towards

### 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:

$$\displaystyle \begin{cases} x + y = \text-2\\x - y = 12\end{cases}$$

The solution to this system is $$x=5$$ and $$y=\text-7$$ because when these values are substituted for $$x$$ and $$y$$, each equation is true: $$5+(\text-7)=\text-2$$ and $$5-(\text-7)=12$$.

### Print Formatted Materials

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