 # Solution Sets to Equations with Two Variables

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Common Core For Algebra I

Examples, videos, and solutions to help Algebra I students learn how to solve equations with two variables.

### New York State Common Core Math Algebra I, Module 1, Lesson 20

Worksheets for Algebra I, Module 1, Lesson 20 (pdf)

Lesson 20 Student Outcomes

Students recognize and identify solutions to two-variable equations. They represent the solution set graphically. They create two variable equations to represent a situation. They understand that the graph of the line ax + by = c is a visual representation of the solution set to the equation ax + by = c.

Lesson 20 Summary

An ordered pair is a solution to a two variable equation when each number substituted into its corresponding variable makes the equation a true number sentence. All of the solutions to a two variable equation are called the solution set.

Each ordered pair of numbers in the solution set of the equation corresponds to a point on the coordinate plane. The set of all such points in the coordinate plane is called the graph of the equation.

Exit Ticket

1. The Math Club sells hot dogs at a school fundraiser. The club earns \$108 and has a combination of five-dollar and one-dollar bills in its cash box. Possible combinations of bills are listed in the table below.

a. Find one more combination of ones and fives that totals \$108.

b. The equation 5x + 1y = 108 represents this situation. A graph of the line y = -x + 108 is shown. Verify that each ordered pair in the table lies on the line.

c. What is the meaning of the variables (x and y) and the numbers (1, 5, and 108) in the equation ?

d. Does the graph make sense in this context?

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