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

2. Unit 1 Day 2 WARM UP (in your spiral)
3x + 4y = - 4
x + 2y = 2
a) How many solutions? Why?
b) Graph the system. SOL:_____

3. Unit 1 Day 2 WARM UP (in your spiral)

4. Math3H - Unit 1 Day 2 SYSTEMS OF LINEAR INEQUALITIES
OBJECTIVES:
1) Graph a linear inequality
2) Graph the solution of a system of
inequalities

5. 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.

6. 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.

7. 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 ≤

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

9. 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

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

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

12. 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.

13. 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)

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

15. 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?

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

17. U1 Day 2 HW On Bb In the HW Folder Unit 1 Day 2 HW Print it or not 
Show all your work for every problem and graph on graph paper!

18. TEACHER NOTES
On Bb
In the Teacher Notes Tab