section 4.5 graphing systems of linear inequalities in two variables
TRANSCRIPT
Section 4.5
Graphing Systems of Linear Inequalities in Two Variables
4.5 Lecture Guide: Graphing Systems of Linear Inequalities in Two Variables
Objective: Graph a linear inequality in two variables.
1. Determine whether each point is a solution of 5 10.x y
(a) 2,1 (b) (c) 2,0 0,0
A solution of a linear inequality in two variables is an ordered pair of values that, when substituted into the inequality, makes a true statement.
Step 1. Graph the equality Ax By C using
(a) A _________________________ line for
Graphing a Linear Inequality
or
(b) A _________________________ line for < or >
Step 2. Choose an arbitrary test point not on the line; 0,0 is often convenient. Substitute this test point into theinequality.
Step 3. (a) If the test point satisfies the inequality, shade thehalf-plane containing this point.
(b) If the test point does not satisfy the inequality, shade the other half-plane.
Graph each linear inequality. Where possible, use your calculator as a check. See Calculator Perspective 4.5.1.
23
5y x 2.
-8
8
-8 8
y
x
3.
-8
8
-8 8
y
x
34
4y x
Graph each linear inequality. Where possible, use your calculator as a check. See Calculator Perspective 4.5.1.
4.
-8
8
-8 8
y
x
3y
Graph each linear inequality. Where possible, use your calculator as a check. See Calculator Perspective 4.5.1.
5.
-8
8
-8 8
y
x
2x
Graph each linear inequality. Where possible, use your calculator as a check. See Calculator Perspective 4.5.1.
Objective: Graph a system of linear inequalities.
To graph a system of linear inequalities, we graph each inequality and then take as our solution the intersection of the regions shaded from each inequality.
Graph the solution of each system of linear inequalities.1
2 4
y x
y x
6.
-8
8
-8 8
y
x
Graph the solution of each system of linear inequalities.
7.
-8
8
-8 8
y
x
2 6
2 10
x y
x y
Graph the solution of each system of linear inequalities.
0
0
2 8 0
2
x
y
x y
x y
8.
-8
8
-8 8
y
x
9. A local school sells student and adult tickets for basketball games. The number of student tickets x and adult tickets y sold each game are both nonnegative, and the gym holds a maximum of 2000 people. Write a system of inequalities that represents this situation and graph the solution of this system.
-3000
3000
-3000 3000
y
x