1. Systems of Inequalities Lesson 3-3
Algebra 2
Systems of Inequalities
Lesson 3-3

2. Goals Goal Rubric To solve a linear systems of linear inequalities.
Level 1 – Know the goals.
Level 2 – Fully understand the goals.
Level 3 – Use the goals to solve simple problems.
Level 4 – Use the goals to solve more advanced problems.
Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary
None

4. Definition
System of linear inequalities - is a set of two or more linear inequalities with the same variables. The solution to a system of inequalities is often an infinite set of points that can be represented graphically by shading.
When you graph multiple inequalities on the same graph, the region where the shadings overlap is the solution region.

5. Solution to a System of Linear Inequalities on a Graph
Graph the solution of the system:
3x + y < 9
2x + 5y  10
The solution will be the set of all points that satisfy both of the inequalities in the system. y x 4
The boundary line is 3x + y = 9.
Solution
The boundary line is
2x + 5y = 10

6. Example: Graph the system of inequalities. y < – 3 y ≥ –x + 2
For y < – 3, graph the dashed boundary line y = – 3, and shade below it.
For y ≥ –x + 2, graph the solid boundary line y = –x + 2, and shade above it.
The overlapping region is the solution region.

7. Example: No solution Solve the system of inequalities by graphing.
Graph both inequalities.
The graphs do not overlap, so the solutions have no points in common and there is no solution to the system.
Answer: No solution.

8. Your Turn: Graph the system of inequalities. x – 3y < 6
For x – 3y < 6, graph the dashed boundary line y = – 2, and shade above it.
For 2x + y > 1.5, graph the dashed boundary line y = –2x + 1.5, and shade above it.
The overlapping region is the solution region.

9. Example: Application
Lauren wants to paint no more than 70 plates for the art show. It costs her at least $50 plus $2 per item to produce red plates and $3 per item to produce gold plates. She wants to spend no more than $215. Write and graph a system of inequalities that can be used to determine the number of each plate that Lauren can make.

10. Example: continued
Let x represent the number of red plates, and let y represent the number of gold plates.
The total number of plates Lauren is willing to paint can be modeled by the inequality x + y ≤ 70.
The amount of money that Lauren is willing to spend can be modeled by x + 3y ≤ 215.
x  0
y  0
The system of inequalities is
x + y ≤ 70
50 + 2x + 3y ≤ 215

11. Practice together with JD

12. Assignment
None 
Enjoy your spring break!!!