Problem 95 - College Algebra Essentials

Question

Explain how to graph the solution set of a system of inequalities.

Step-by-Step Solution

Answer

To graph the solution set of a system of inequalities, each inequality needs to be graphed individually by finding its line of equality and shading the region corresponding to the inequality sign. The solution set of the system is then found at the intersection of all the shaded regions, which represents the points satisfying all inequalities simultaneously.

Step 1: Understanding Basic Principles

The first step is to understand that the solution to a system of inequalities is the intersection of the solution sets of each inequality. It is the set of points that satisfy all inequalities at once. Also, when dealing with inequalities, it's important to keep the 'less than or equal to' format.

Step 2: Graphing Each Inequality

Next, each inequality should be graphed separately. Start by temporarily looking at the inequality as an equality to draw a line. Then, depending on the inequality sign, shade the region either above or below that line. If the inequality is 'less than or equal to' or 'greater than or equal to', the line should be solid. If not, the line is dashed.

Step 3: Finding the Solution Set

Lastly, the solution set is found at the intersection of the shaded regions of all inequalities. This is the area that satisfies all the inequalities at the same time. Highlighting this area on the graph identifies the possible solutions to the system of inequalities.