1. How do you model a problem in which two or more equations have solutions that are constrained? For example, how can you find the range of scores you need on a college entrance exam in order to get into the college of your choice?

2. In this lesson you will learn how to represent solutions and constraints to systems of linear inequalities by graphing.

3. Let’s Review You can graph an inequality in two variables. 5x + 6y ≤ 30

4. A Common Mistake Shading the wrong half-plane 5x + 6y ≤ 30 Let me check by using the point (0, 0). Oops! It looks like I shaded the wrong half plane

5. Core Lesson A college entrance exam has two parts: a verbal part and a mathematics part. You can score a maximum of 800 points per section. Admission requirements: at least 600 on the math part and at least 1100 total What is the range of scores needed?

6. x + y ≤ 1600 (math score)(verbal score) + ≤ 1600 math score ≥ 600x ≥ 600 x + y ≥ 1100 math score reading score

7. In this lesson you have learned how to represent solutions and constraints to systems of linear inequalities by graphing.

8. Guided Practice A movie director needs at least 40 extras for a scene at a summer camp. She cannot use more than 30 children. Write and graph a system of linear inequalities to show solutions for this problem. Then find at least two different pairs of children and adults that the director could use.

9. Extension Activities Suppose you have $35 to spend on an ice cream social. You can buy ice cream by the ounce at your local ice cream store, and you want to buy two different flavors. Write and graph a system of linear inequalities to model this problem. Then find at least two different solutions to this problem.

10. Suppose your school is selling T-shirts and hats as a fundraiser. You can order no more than a total of 500 items and spend no more than $600. You pay $2 per hat and sell each hat for $3.50. You pay $0.75 per T-shirt and sell each T-shirt for $1.50. What combination do you need to sell in order to maximize your profit? What is your maximum profit?

11. Quick Quiz You want to bake at least 6 and at most 11 pies for a bake sale. You want at least twice as many apple pies as lemon meringue pies. Write and graph a system of linear inequalities to model the situation.

12. The Student Government wants to set up a Prom Committee with juniors and seniors. The committee needs between 7 and 10 members. The number of seniors should be greater than the number of juniors. Write and graph a system of linear inequalities to model the problem.