
To find: find the coordinates of all vertices and determine whether the solution set bounds or not.

Answer to Problem 42E
The system has no solution
Explanation of Solution
Given:
Calculation:
Consider the system of inequalities
Sketch the graph of the solution of the system of inequalities.
Step 1: Graph the lines that corresponds to each inequality
To graph the inequality
Clearly, the points on the line itself do not satisfy the inequality because. the inequality contains
To graph the inequality
Clearly, the points on the line itself do not satisfy the inequality because. the inequality contains
To graph the inequality
Clearly, the points on the line itself do not satisfy the inequality because. the inequality contains
Step 2: To determine whether which region satisfies the inequalities, use the test point
Substitute the coordinates of the point
The computations are tabulated as shown below:
Inequality | Test point
| Conclusion |
Not a part of the graph | ||
Not a part of the graph | ||
Part of the graph |
From the above table, observe that
1. The point
the dashed line that does not contain the point
2. The point
the dashed line that does not contain the point
3. The point
The graph of the solution of the system of inequalities is shown below:
From the graph, observe that there is no common shaded region for the given system.
Therefore, the system [has no solution].
Conclusion: the system has no solution
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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