6-6 Systems of Linear Inequalities
6-6 Systems of Linear Inequalities MATH 8 PLUS MR. DIXON
Vocabulary System of Linear Inequalities: is made up of two or more linear inequalities.
Solution of a System of linear inequalities: an ordered pair that makes all the inequalities in the system true.
Example #1; Graphing a System of Inequalities What is the graph of the system?
y > -x + 5 - 3x + y < - 4
Rewrite the second inequality y < 3x - 4 Then Graph both inequalities. The system’s solutions lie in the dark pink region where the graphs overlap.
Example #2; Writing a System of Inequalities From a Graph Step 1: Find the slope and y-intercept of each line. Step 2: Write the inequality for both lines. Remember that a < or > is used for a dashed line. And, < or > is use for a solid line.
Solid Line:
m = 1/2 b = 1
Dashed Line: m = - 1/2 b = 1
y < 1/2x + 1 y < - 1/2x + 1
Example #3; Using a System of Inequalities You can model many real world situations by writing and graphing systems of linear inequalities. Some real world situations involved three or more restrictions, so you must write a system of a least three inequalities. You want to build a fence for a rectangular dog run. You want the run to be at least 10 ft wide. The run can be at most 50 ft long. You have 126ft of fencing. What is a graph showing the possible dimensions of the dog run? Let x = the width of the dog run
Let y = the length of the dog run
Remember the dog run must have fencing on all four sides. 2x + 2y < 126
x > 10
y < 50
Example #3; Continued
80 70
2x + 2y < 126 2y < - 2x + 126
x > 10 y < 50
y < - x + 63 Possible Dimensions: Answers may vary Width = 20 ft; length = 43 ft
L E N G T H (ft)
60
50 40 30 20 10
Width = 30 ft; length = 30 ft Width = 25 ft; length = 38 ft
10
20
30
40
50
Width (ft)
60
70
80
Assignment Pg. 399 (7 – 27) All Use grid paper to make neat graphs.
Make sure you shade the overlapping (true solutions) darker. Use a ruler to make straight lines.
Vocabulary System of Linear Inequalities: is made up of two or more linear inequalities.
Solution of a System of linear inequalities: an ordered pair that makes all the inequalities in the system true.
Example #1; Graphing a System of Inequalities What is the graph of the system?
y > -x + 5 - 3x + y < - 4
Rewrite the second inequality y < 3x - 4 Then Graph both inequalities. The system’s solutions lie in the dark pink region where the graphs overlap.
Example #2; Writing a System of Inequalities From a Graph Step 1: Find the slope and y-intercept of each line. Step 2: Write the inequality for both lines. Remember that a < or > is used for a dashed line. And, < or > is use for a solid line.
Solid Line:
m = 1/2 b = 1
Dashed Line: m = - 1/2 b = 1
y < 1/2x + 1 y < - 1/2x + 1
Example #3; Using a System of Inequalities You can model many real world situations by writing and graphing systems of linear inequalities. Some real world situations involved three or more restrictions, so you must write a system of a least three inequalities. You want to build a fence for a rectangular dog run. You want the run to be at least 10 ft wide. The run can be at most 50 ft long. You have 126ft of fencing. What is a graph showing the possible dimensions of the dog run? Let x = the width of the dog run
Let y = the length of the dog run
Remember the dog run must have fencing on all four sides. 2x + 2y < 126
x > 10
y < 50
Example #3; Continued
80 70
2x + 2y < 126 2y < - 2x + 126
x > 10 y < 50
y < - x + 63 Possible Dimensions: Answers may vary Width = 20 ft; length = 43 ft
L E N G T H (ft)
60
50 40 30 20 10
Width = 30 ft; length = 30 ft Width = 25 ft; length = 38 ft
10
20
30
40
50
Width (ft)
60
70
80
Assignment Pg. 399 (7 – 27) All Use grid paper to make neat graphs.
Make sure you shade the overlapping (true solutions) darker. Use a ruler to make straight lines.
