Embed Size (px)
Citation preview
System of linear inequalities
System of linear inequalities
A system of linear inequalities is made up of two or more inequalities
A solution of a System of linear inequalities is an ordered pair that makes all the inequalities in the system true
The graph of a system of inequalities is the set of the points that represent all of the solutions of the system
Notes:
System of linear inequalities
Graphing a System of linear inequalities
What is the graph of the system? y 2x – 32x + y 2
Step 1: graph y 2x – 3
Step 2: graph 2x + y 2
The system’s solutions lie in the green region where the graphs overlap
1
2
3
4
1 2 3 4 5-1
-2
-3
The green regionrepresents solution ofboth inequalities
The yellow regionrepresents solution ofy 2x - 3
The blue regionrepresents solution of2x + y 2
Check: (3,0) is in green region. See if (3,0) satisfies both inequalities
y 2x – 30 2(3) – 30 3
2x + y 22(3) + 0 26 2
Writing a System of linear inequalities from a graph
What system of linear inequalities is represented by graph ?
Write the inequality that represents the yellow region. Then Write the inequality that represents the blue region
Using a System of linear inequalities
You are planning what to do after school. You can spend at most 6 h daily playing basketball and doing homework. You want to spend less than 2 h playing basketball. You must spend at least 2 h on homework. What is a graph showing how you can spend your time?
At most 6 h playing basketball and doing homeworkLess than 2 h playing basketballAt least 2 h doing homework
What do you know? What do you need?
To find different ways you can spend your time
What do have to do?
Write and graph an inequality for each restriction.
Find the region where all three restrictions are met
Let x = the number of hours playing basketball
Write a system of inequalities
x+ y 6 At most 6 h of basketball and homework
Let y = the number of hours doing homework
x 2 Less than 2 h of basketball
y 2 At least 2 h of homework
1
2
3
4
1 2 3 4 5
5
6
6 7
Using a System of linear inequalities
Graph the system
You are planning what to do after school. You can spend at most 6 h daily playing basketball and doing homework. You want to spend less than 2 h playing basketball. You must spend at least 2 h on homework. What is a graph showing how you can spend your time?
x+ y 6 At most 6 h of basketball and homework x 2 Less than 2 h of basketbally 2 At least 2 h of homework
Important: Because the time cannot be negative the graph makes sense only in the first quadrant.
Remember:The solutions of the system are all the points in the shaded region including the points on the solid boundary lines
x+ y 6
x 2
y 2
Hours of Basketball, x
Ho
urs
of
Ho
me
wo
rk,
y
After-School Activities
Using a System of linear inequalities
You want to build a fence for a rectangular dog run. You want the run be at least 10 feet wide. The run can be at most 50 feet long. You have 126 ft of fencing. What is a graph showing the possible dimensions of the dog run?
At most 126 ft of fenceAt most 50 feet longAt least 10 feet wide
What do you know? What do you need?
Possible dimensions of the dog run
What do have to do?
Write and graph an inequality for each restriction.
Find the region where all three restrictions are met
Write a system of inequalities
2x+ 2y 126 At most 126 ft of fence
Let y = the wide of the dog run
x 50 At most 50 feet long
y 10 At least 10 feet wide
You turn
Let x = the long of the dog run
RECTAGLE PERIMETER FORMULA
2l + 2w
Using a System of linear inequalities
Graph the system
Important: Because the distance cannot be negative the graph makes sense only in the first quadrant.
Remember:The solutions of the system are all the points in the shaded region including the points on the solid boundary lines
x+ y 6
x 50
y 10
Dog run long, x
Do
g r
un
wid
e,
y
Dog Run fence
You want to built a fence for a rectangular dog run. You want the run be at least 10 feet wide. The run can be at most 50 feet long. You have 126 ft of fencing. What is a graph showing the possible dimensions of the dog run?
2x+ 2y 126 At most 126 ft of fencex 50 At most 50 feet longy 10 At least 10 feet wide
10
20
30
40
10 20 30 40 50
50
60
60 70
Using a System of linear inequalities
An arena contains 1200 seats. For an upcoming concert, tickets will be priced $12.00 for some seats and $10.00 for others. At least 500 tickets are to be priced at $10.00, and the total sales must be at least $7200 to make a profit. What are the possible ways to price the tickets?
At most 1200 seatsAt most 50 feet longAt least 500 tickets at $10
What do you know? What do you need?
Possible ways to price the tickets
What do have to do?
Write and graph an inequality for each restriction.
Find the region where all three restrictions are met
Write a system of inequalities
2x+ 2y 126 At most 126 ft of fence
Let y = $ 10 tickets
x 50 At most 50 feet long
y 10 At least 10 feet wide
More practice
Let x = $ 12 tickets
