Solution Sets to Inequalities with Two Variables

Examples, videos, and solutions to help Algebra I students learn how to find solution sets to two-variable inequalities.

New York State Common Core Math Algebra I, Module 1, Lesson 21

Worksheets for Algebra 1

Student Outcomes

Students recognize and identify solutions to two-variable inequalities. They represent the solution set graphically. They create two variable inequalities to represent a situation.

Students understand that a half-plane bounded by the line is a visual representation of the solution set to a linear inequality such as . They interpret the inequality symbol correctly to determine which portion of the coordinate plane is shaded to represent the solution.

Lesson Summary

An ordered pair is a solution to a two variable inequality if, when each number is substituted into its corresponding variable, it makes the inequality a true number sentence.
Each ordered pair of numbers in the solution set of the inequality corresponds to a point on the coordinate plane.

The set of all such points in the coordinate plane is called the graph of the inequality.

The graph of a linear inequality in the coordinate plane is called a half-plane.

Exit Ticket

What pairs of numbers satisfy the statement: The sum of two numbers is less than 10?

Create an inequality with two variables to represent this situation and graph the solution set.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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