Review graphinig inequalities Graph systems of inequalities

1. 9.6 Systems of Inequalities
Chapter 9 Systems and Matrices

2. Concepts and Objectives
⚫ Systems of Inequalities
⚫ Graph systems of inequalities
⚫ Identify solutions to systems of inequalities

3. Graphing Review
⚫ To graph a linear inequality, put the inequality into
slope-intercept form.
⚫ Plot the y-intercept and count the slope from there
(rise over run)
Symbol Line Shade
< below
> above
 below
 above

4. Graphing Review
⚫ Example: Graph the solution to + 2 3 6x y

5. Graphing Review
⚫ Example: Graph the solution to + 2 3 6x y
 − +3 2 6y x
 − +
2
2
3
y x

6. Graphing Review
⚫ Example: What is the solution to ? −2
2y x

7. Graphing Review
⚫ Example: What is the solution to ?
Vertex: (0, –2)
 −2
2y x

8. Systems of Inequalities
⚫ The solution to a system of inequalities will be the graph
of the overlap between the two (or more) inequalities.
⚫ You must graph the system to show the solution.
⚫ If the inequalities do not overlap, then there is no
solution to the system.

9. Systems of Inequalities
⚫ Example: What is the solution to the system?
−  −

+ 
2 4
3 2
x y
x y

10. Systems of Inequalities
⚫ Example: What is the solution to the system?
Inequality #1:
−  −

+ 
2 4
3 2
x y
x y
−  − −2 4y x
 +
1
2
2
y x

11. Systems of Inequalities
⚫ Example: What is the solution to the system?
Inequality #2:
−  −

+ 
2 4
3 2
x y
x y
 − +3 2y x

12. Systems of Inequalities
⚫ Example: What is the solution to the system?
 − 

+ 
2
1
3 2 4
x y
x y

13. Systems of Inequalities
⚫ Example: What is the solution to the system?
Inequality #1
 − 

+ 
2
1
3 2 4
x y
x y
−  − +2
1y x
 −2
1y x

14. Systems of Inequalities
⚫ Example: What is the solution to the system?
Inequality #2
 − 

+ 
2
1
3 2 4
x y
x y
 − +2 3 4y x
 − +
3
2
2
y x

15. Classwork
⚫ College Algebra (9.6 Assignment)
⚫ Page 904: 12-16 (even), page 876: 36-46 (even),
page 850: 48-52 (even)