Question

select the correct answer from each drop - down menu.
a system of two linear inequalities is graphed as shown, where the solution region is shaded.
complete the sentences below by determining whether each point is, or is not, located in the solution region.
the point (-3,2) ■ located in the solution region.
the point (-7,5) ■ located in the solution region.
the point (2,-5) ■ located in the solution region.
the point (-14,6) ■ located in the solution region.

Explanation:

To determine if a point is in the solution region, we check if it lies within the shaded area defined by the two linear inequalities.

Step 1: Analyze the point (-3, 2)

• Locate (-3, 2) on the graph. The shaded region includes this point as it is in the overlapping (or relevant shaded) area. So, (-3, 2) is in the solution region.

Step 2: Analyze the point (-7, 5)

• Locate (-7, 5). This point is within the shaded region (checking the graph's shading and the position relative to the lines). So, (-7, 5) is in the solution region.

Step 3: Analyze the point (2, -5)

• Locate (2, -5). This point is not in the shaded region (the shading does not cover this area based on the graph's lines and shading). So, (2, -5) is not in the solution region.

Step 4: Analyze the point (-14, 6)

• Locate (-14, 6). This point is within the shaded region (considering the graph's boundaries and shading). So, (-14, 6) is in the solution region.

Answer:

• The point (-3,2) is located in the solution region.
• The point (-7,5) is located in the solution region.
• The point (2,-5) is not located in the solution region.
• The point (-14,6) is located in the solution region.