Sketch the graph of the solution set of system of inequalities and label the vertices of the region.
Answer to Problem 31E
The graph for the first inequality is the half-plane to the left of the line (1)
The graph for the second inequality is the half-plane lying to the right of the line (2)
The graph for the third inequality is the half-plane lying above 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),
On adding these two equations,
Replace the value of
Therefore, the point of intersection is (0, 1).
Now, solve equations (1) and (3)
Thus,
Therefore, the point of intersection is (-1, 0)
The graph for the first inequality is the half-plane to the left of the line (1).
The graph for the second inequality is the half-plane lying to the right of the line (2)
The graph for the third inequality is the half-plane lying above 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
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning