To find: whether the solution of linear inequalities to be all real numbers.
Answer to Problem 41E
The solution set of system of inequalities can be half plane only at most therefore, the answer is no.
Explanation of Solution
Given:
Linear inequalities.
Concept used:
If the inequality state something true there is no solution.
If an inequality would be true for all positive values, the answer is all real numbers.
Calculation:
Consider the below sentence.
Is it possible for the solution set of system of linear inequalities to be all real numbers.
Answer the above question by giving a reason.
The solution set of system of linear inequalities cannot be all real numbers. The reason is as explained in the below steps.
System of inequalities contain more than one inequality.
Each inequality represents half plane.
The solution set of inequalities will be the intersection of all solution of all the inequalities.
Hence, the solution set of system of inequalities can be half plane only at most therefore, the answer is no.
Chapter 5 Solutions
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