Question

for the graph below determine if each point is a solution to the system or not.
a
b
c
d
yes no

Explanation:

Step1: Recall solution region rules

A solution to a system of inequalities (from the graph) lies in the overlapping shaded region. Check each point's position relative to the shaded area and the lines (solid line: included, dashed line: not included).

Step2: Analyze Point A

Point A is at (2, 4). The shaded region is below the solid line and above the dashed line? Wait, looking at the graph: the shaded area is between the two lines? Wait, the solid line is the boundary (included), dashed is excluded. Point A is above the shaded region (since shaded is lower, A is in unshaded). So A: No.

Step3: Analyze Point B

Point B is on the solid line. Solid lines are part of the solution (since the line is solid, indicating equality is included). So B: Yes.

Step4: Analyze Point C

Point C is on the dashed line. Dashed lines mean the boundary is not included in the solution. So C: No.

Step5: Analyze Point D

Point D is inside the shaded region (between the two lines, in the gray area). So D: Yes.

Answer:

A: No
B: Yes
C: No
D: Yes