Sketch the graph of the solution set of system of inequalities and label the vertices of the region.
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
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning