1. Solving Systems of Linear Inequalities
Algebra 6.6
Solving Systems of Linear Inequalities

2. Learning Targets Language Goal
Students will be able to graph systems of linear inequalities in two variables.
Math Goal
Students will be able to graph and solve systems of linear inequalities in two variables.
Essential Questions
How do we know where to shade in our graph of a system of linear inequalities?

3. Warm-up

4. Homework Check

5. Homework Check

6. Vocabulary
System of Linear Inequalities:
a set of two or more linear inequalities containing two or more variables.
Solution of a System of Linear Inequalities:
all of the ordered pairs that satisfy all the linear inequalities in the system.

7. Example 1: Identifying Solutions of Systems of Linear Inequalities
Tell whether the ordered pair is a solution of the inequality. A. (2, 1) 𝑦<−𝑥+4 𝑦≤𝑥+1 B. (2, 0) 𝑦≥2𝑥 𝑦<𝑥+1

8. Example 1: Identifying Solutions of Systems of Linear Inequalities
Tell whether the ordered pair is a solution of the inequality. C. (0, 1) 𝑦<−3𝑥+2 𝑦≥𝑥−1 D. (0, 0) 𝑦>−𝑥+1 𝑦>𝑥−1

9. Graphing Systems of Linear Inequalities
1. Graph the first inequality. Remember dotted and solid lines and shading.
2. Graph the second inequality on the same coordinate plane including shading.
3. Then find where the two shadings overlap. This is your solutions!

10. Example 2: Solving a system of Linear Inequalities by Graphing
Graph the system of linear inequalities. Give two ordered pairs that are solutions.
A. 8𝑥+4𝑦≤12 𝑦< 1 2 𝑥−2
Order pair solutions ______ ______

11. Example 2: Solving a system of Linear Inequalities by Graphing
Graph the system of linear inequalities. Give two ordered pairs that are solutions.
B. 𝑦>2 𝑦≤𝑥+1
Order pair solutions ______ ______

12. Example 2: Solving a system of Linear Inequalities by Graphing
Graph the system of linear inequalities. Give two ordered pairs that are solutions.
C. 𝑦>𝑥−7 3𝑥+6𝑦≤12
Order pair solutions ______ ______

13. Example 3: Graphing Systems with Parallel Boundaries
Graph the system of linear inequalities..
A. 𝑦<2𝑥−3 𝑦>2𝑥+2

14. Example 3: Graphing Systems with Parallel Boundaries
Graph the system of linear inequalities..
B. 𝑦≤𝑥+1 𝑦>𝑥−3

15. Example 3: Graphing Systems with Parallel Boundaries
Graph the system of linear inequalities..
C. 𝑦≤3𝑥−2 𝑦≤−3𝑥+4

16. Example 4: Word Problems
A. A surf show makes the profits given in the table. The shop owner sells at least 10 surfboards and at least 20 wakeboards per month. He wants to earn at least $2000 a month. Show and describe all possible combinations of surfboards and wakeboards that the store owner needs to sell to meet his goals. List two possible combinations.
1. Write a system of inequalities. Let x represent the number of
surfboards and y represent the number of wakeboards.
2. Graph the system. The graph should be in the first quadrant
because sales are not negative.
3. Describe all possible combinations.
4. List two possible combinations.
Surfboard
150
Wakeboard
100
Order pair solutions ______ ______

17. Example 4: Word Problems
B. At her party, Alice is serving pepper jack cheese and cheddar cheese. She wants to have at least 2 pounds of each. Alice wants to spend at most $20 on cheese. Show and describe all possible combinations of the two cheeses Alice could buy. List two possible combinations.
Order pair solutions ______ ______

18. Graphing With Style WS

19. Graphing With Style WS

20. Lesson Quiz