To state and Justify:
Whether the solution of a set of linear inequalities is the union or the intersection of individual linear inequalities.
The solution of a set of linear inequalities is the intersection of individual linear inequalities.
Concepts Used:
Solving a system of linear inequalities.
Intersection and union of the set.
Description:
The solution of a set of linear inequalities is the intersection of individual linear inequalities.
By definition a solution of the system needs to satisfy each condition simultaneously. So only those solutions which belong to the solution set of all the inequalities of the system are the solutions of the system. Such solutions are members of the intersection of individual solution sets. A union of individual solution sets, on the other hand, will include solutions that may not satisfy all the inequalities and hence cannot be called the solution of the system.
Chapter 3 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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