1. Math3H - Unit 2 Day 2 SYSTEMS OF LINEAR INEQUALITIES
Solving Linear Systems of Inequalities by Graphing

2. Math3H - Unit 2 Day 2 SYSTEMS OF LINEAR INEQUALITIES
OBJECTIVES:
1) Apply systems of equations to real
world situations
2) Graph a linear inequality
3) Graph the solution of a system of
inequalities

3. Applications of System of Equations
Example 1: A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

4. Example 2: The senior classes at Panther Creek High School and Enloe HS planned separate trips to New York City. The senior class at PCHS rented and filled 1 van and 6 buses with 372 students. EHS rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students.

5. Example 3: Matt and Ming are selling fruit for a school fundraiser
Example 3: Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.

6. Solving Systems of Linear Inequalities
We show the solution to a system of linear inequalities by graphing them…Why is that?
This process is easier if we put the inequalities into Slope-Intercept Form, y = mx + b.
The < > sign will tell us how to shade the graph.

7. Solving Systems of Linear Inequalities
Graph the line using the y-intercept & slope.
If the inequality is < or >, make the lines dotted
If the inequality is < or >, make the lines solid.

8. Solving Systems of Linear Inequalities
The solution also includes points not on the line, so you need to shade the region of the graph:
Shade above for
y > or y 
Shade below for
y < or y ≤

9. Solving Systems of Linear Inequalities
Example:
a: 3x + 4y > - 4
b: x + 2y < 2
Put in Slope-Intercept Form:

10. Solving Systems of Linear Inequalities
Example, continued:
Graph each line, make dotted or solid and shade the correct area. a:
dotted
shade above b:
dotted
shade below

11. Solving Systems of Linear Inequalities
a: 3x + 4y > - 4

12. Solving Systems of Linear Inequalities
a: 3x + 4y > - 4
b: x + 2y < 2

13. Solving Systems of Linear Inequalities
a: 3x + 4y > - 4
b: x + 2y < 2
The area between the green arrows is the region of overlap and thus the solution.

14. Checking your Solution
a: 3x + 4y > - 4
b: x + 2y < 2
Choose a test point in the solution region and check it in both equations – ex. (0, 0)

15. Checking your Solution
a: 3x + 4y > - 4
b: x + 2y < 2
3*0 + 4*0 > -4
0 + 2*0 < 2
Both are TRUE!

16. You try it! Example 2: x + 2y > -12 -3x + y < 8
Put in Slope-Intercept Form
Graph…solid or dotted?
shade above or below?
c) Solution area?

17. Unit 2 Quiz 1 Day 1 and 2 only You should be able to:
Tell how many solutions
Solve systems of equations and inequalities

18. U2 Day 2 HW
In Weebly

19. TEACHER NOTES
In Weebly