2. ESSENTIAL QUESTIONS
• How do you write a system of linear inequalities for a given
graph?
• How do you graph the solution set of a system of linear
inequalities?
• Where you’ll see this:
• Sports, entertainment, retail, finance
3. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
y < 2x + 3 y ≥ −3x + 4
4. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
y < 2x + 3 y ≥ −3x + 4
5. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
y < 2x + 3 y ≥ −3x + 4
6. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
y < 2x + 3 y ≥ −3x + 4
7. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
y < 2x + 3 y ≥ −3x + 4
8. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
y < 2x + 3 y ≥ −3x + 4
9. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
y < 2x + 3 y ≥ −3x + 4
10. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
y < 2x + 3 y ≥ −3x + 4
11. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
y < 2x + 3 y ≥ −3x + 4
12. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
13. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
14. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
15. EXAMPLE 1
Graph the following linear inequalities on separate
coordinates, then again on the same coordinates.
16. EXAMPLE 2
Write a system of linear inequalities for the graph shown.
17. EXAMPLE 2
Write a system of linear inequalities for the graph shown.
y ≥ −4x + 6
1
y < x − 3
2
18. EXAMPLE 3
Matt Mitarnowski was planning a wedding reception
that will last at least 4 hours. The couple wants to
hire a band that charges $300 per hour and a DJ that
charges $150 per hour. They want to keep the music
expenses under $1200. The band and DJ charge by
the whole hour only.
a. Write a system of linear inequalites that models the
situation.
19. EXAMPLE 3
Matt Mitarnowski was planning a wedding reception
that will last at least 4 hours. The couple wants to
hire a band that charges $300 per hour and a DJ that
charges $150 per hour. They want to keep the music
expenses under $1200. The band and DJ charge by
the whole hour only.
a. Write a system of linear inequalites that models the
situation.
x = DJ, y = band
20. EXAMPLE 3
Matt Mitarnowski was planning a wedding reception
that will last at least 4 hours. The couple wants to
hire a band that charges $300 per hour and a DJ that
charges $150 per hour. They want to keep the music
expenses under $1200. The band and DJ charge by
the whole hour only.
a. Write a system of linear inequalites that models the
situation.
x = DJ, y = band
Time:
21. EXAMPLE 3
Matt Mitarnowski was planning a wedding reception
that will last at least 4 hours. The couple wants to
hire a band that charges $300 per hour and a DJ that
charges $150 per hour. They want to keep the music
expenses under $1200. The band and DJ charge by
the whole hour only.
a. Write a system of linear inequalites that models the
situation.
x = DJ, y = band
Time: x + y ≥ 4
22. EXAMPLE 3
Matt Mitarnowski was planning a wedding reception
that will last at least 4 hours. The couple wants to
hire a band that charges $300 per hour and a DJ that
charges $150 per hour. They want to keep the music
expenses under $1200. The band and DJ charge by
the whole hour only.
a. Write a system of linear inequalites that models the
situation.
x = DJ, y = band
Time: x + y ≥ 4
Money:
23. EXAMPLE 3
Matt Mitarnowski was planning a wedding reception
that will last at least 4 hours. The couple wants to
hire a band that charges $300 per hour and a DJ that
charges $150 per hour. They want to keep the music
expenses under $1200. The band and DJ charge by
the whole hour only.
a. Write a system of linear inequalites that models the
situation.
x = DJ, y = band
Time: x + y ≥ 4
Money: 150x + 300y <1200
24. EXAMPLE 3
Matt Mitarnowski was planning a wedding reception
that will last at least 4 hours. The couple wants to
hire a band that charges $300 per hour and a DJ that
charges $150 per hour. They want to keep the music
expenses under $1200. The band and DJ charge by
the whole hour only.
a. Write a system of linear inequalites that models the
situation.
x = DJ, y = band
x + y ≥ 4
Time: x + y ≥ 4
150x + 300y <1200
Money: 150x + 300y <1200
25. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
26. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x+y≥4
27. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x+y≥4
−x −x
28. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x+y≥4
−x −x
y ≥ −x + 4
29. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x+y≥4 150x + 300y <1200
−x −x
y ≥ −x + 4
30. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4
31. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
32. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
33. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
1
y <− x+4
2
34. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
1
y <− x+4
2
35. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
1
y <− x+4
2
36. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
1
y <− x+4
2
37. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
1
y <− x+4
2
38. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
1
y <− x+4
2
39. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
1
y <− x+4
2
40. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
1
y <− x+4
2
41. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
1
y <− x+4
2
42. EXAMPLE 3
b. Solve the system by graphing.
x + y ≥ 4
150x + 300y <1200
x + y ≥ 4 150x + 300y <1200
−x −x −150x −150x
y ≥ −x + 4 300y < −150x +1200
300 300
1
y <− x+4
2