Problem 94 - Algebra and Trigonometry

Question

What is a solution of a system of linear inequalities?

Step-by-Step Solution

Answer

A solution to a system of linear inequalities is the region where the graphs of all inequalities in the system overlap.

Step 1: Understand Linear Inequality

Each inequality can be viewed as a half-plane, represented graphically. A half-plane is the area on one side of a line on a graph. An inequality determines which side of a boundary line a solution lies.

Step 2: Understand System of Linear Inequalities

A system of linear inequalities is a set of inequalities with the same variables. The solution is the set of all points that make all the inequalities in the system true.

Step 3: Find the Common Region

In order to find the solution, each inequality needs to be graphed on the same set of axes and the common region, the area where all the half-planes overlap, is identified. This common or overlapping region is the solution to the system of linear inequalities.