m3 1.5 systems of linear inequalities m3 1.5 systems of linear inequalities essential questions: how...
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M3 1.5 Systems of Linear M3 1.5 Systems of Linear InequalitiesInequalities
M3 1.5 Systems of Linear M3 1.5 Systems of Linear InequalitiesInequalities
Essential Questions: •How can we write and graph a system of linear inequalities in two variables?•How can we write a system of linear inequalities in two variables for a given solution region?
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Example 1Graph the system.
x 0
y 0
y 3x 2
y x 4
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Example 1Graph the system.
x 0
y 0
y 3x 2
y x 4
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Example 2Graph the system.
y 2x 2
1y x 1
2x 3
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Example 2Graph the system.
y 2x 2
1y x 1
2x 3
x 0
y 0
y x 2
y 2x 3
Graph the system.
Example 4Graph the linear inequality.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
5 x 3
x 3x 5
Example 4Graph the linear inequality.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
5 x 3
x 3x 5
Example 5Graph the linear inequality.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
4 y 2
y 2y 4
Example 5Graph the linear inequality.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
4 y 2
y 2y 4
Homework
p. 25-26 # 1-27 odds