Which region represents the solutions of the following system of inequality?x ≥ y and x ≤ -y Region II including the boundary lines. Region IV including the boundary lines. Region III including the boundary lines. Region I including the boundary lines.

The system of inequalities given is x ≥ y and x ≤ -y.

Step 1: Understand the inequalities The first inequality x ≥ y is the region above the line y = x, including the line itself. The second inequality x ≤ -y is the region below the line y = -x, including the line itself.

Step 2: Draw the inequalities on a graph If you draw these two inequalities on a graph, you will see that the line y = x divides the graph into two regions: Region I (above the line) and Region III (below the line). Similarly, the line y = -x divides the graph into two regions: Region II (to the right of the line) and Region IV (to the left of the line).

Step 3: Identify the common region The common region that satisfies both inequalities is the region that is both above the line y = x and below the line y = -x. This is Region IV including the boundary lines.