EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Question
Chapter 7.5, Problem 33E
To determine
Sketch the graph of the solution set of system of inequalities and label the vertices of the region.
Expert Solution & Answer
Answer to Problem 33E
The graph for the first inequality is the set of all points lying to the right of the line (1)
The graph for the second inequality is the half-plane lying below the line (2)
The graph for the third inequality is the half-plane lying to the left the line (3)
Explanation of Solution
Given:
The system of linear inequalities is:
Now, find the points of each pair of equations.
First, solve equations (1) and (2),
Multiply equation (2) by 3 and add to equation (1)
Adding these two equations
Replace the value of y in equation (2)
Therefore, the point of intersection is (-2, 0).
Multiply equation (3) by -2 and add to equation (1)
On adding these two equations
Replace the value of x in equation (3)
Therefore, the point of intersection is (0, 3)
Multiply equation (2) by -2 and add to equation (3)
On adding these two equations
Replace the value of y in equation (3)
Therefore, the point of intersection is
The graph for the first inequality is the set of all points lying to the right of the line (1).
The graph for the second inequality is the half-plane lying below the line (2)
The graph for the third inequality is the half-plane lying to the left of the line (3)
Therefore, the graph with the solution set of the system of inequalities is shown below:
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
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