# Application of Linear Systems of Inequalities

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## Objective

SWBAT solve real world scenarios using linear systems of inequalities.

#### Big Idea

Students will analyze the coordinates of solutions to linear inequalities that arise from a real-world scenario.

## Do-Now

10 minutes

Students will practice solving systems of linear equations in today's Do Now. As students are working I will pass back the graded Exit Cards from our last class.

Three students will come up to the board to display their responses for the class. Next a student will read the objective, "SWBAT solve real world scenarios using systems of inequalities".

## Whole Group Practice

45 minutes

Using Guided Notes, students will solve linear systems of inequalities. By this point in the year students will have solved many Algebraic word problems. Today's task should feel familiar.

Example One: I will ask the class to read the prompt first, and then underline the information that we will need to construct 2 inequalities. Once we have created our system, I will ask students to graph it on their paper.

The best part of this lesson lies in the analysis of each solution set. Once the system has been graphed, I will probe students understanding  by asking them to fully answer each prompt:

• In this Example we have two variables, x and y. Reread the prompt. What does each variable represent?
• Lets label some points that are in the solution set. Do these points have anything in common.
• Since we know what our variables are representing, what would the point (5, 3) mean in the context of this problem?
• What does the word "constraint" mean? What constraints do we have in this example?
• Name combinations of the possible choices Jade has given her constraints.
• How many weeks can Jade withdrawal money?

Students will work with a partner in 10 minute time-chunks to complete the remaining examples. We will review responses as a whole group at the end of each chunk, with heavy emphasis on analyzing possible solutions, and using the graph to choose the best answer.

## Closing

25 minutes

Students will spend the 15 minutes at the end of class to answer Systems of Inequalities questions with Promethean clickers. I will keep score as we answer each question, giving students a point for every question answered that 85% of students got correct.

Students will then complete an Exit Card.