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
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