# Lesson 13

Systems of Equations

### Lesson Narrative

This lesson formally introduces the concept of system of equations with different contexts. Students recognize that they have found solutions to systems of equations using graphing in the past few lessons by examining the intersection of graphed lines. The next activity introduces students to a system that has no solution and asks them to recognize this by connecting the concepts of parallel lines having no intersection points to the algebraic representations having no common solution.

### Learning Goals

Teacher Facing

• Comprehend that solving a system of equations means finding values of the variables that makes both equations true at the same time.
• Coordinate (orally and in writing) graphs of parallel lines and a system of equations that has no solutions.
• Create a graph of two lines that represents a system of equations in context.

### Student Facing

Let’s learn what a system of equations is.

### Required Preparation

Provide access to straightedges for students to accurately draw graphs of lines.

### Student Facing

• I can explain the solution to a system of equations in a real-world context.
• I can explain what a system of equations is.
• I can make graphs to find an ordered pair that two real-world situations have in common.

### 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 $$5-(\text-7)=12$$.