Question

is (0,0) a solution to the system?

solution
not a solution

Explanation:

Identify the point on the graph

Using the Ordered Pairs knowledge point
The point of interest is the origin, \( (0,0) \). On the coordinate plane, this is where the horizontal x-axis and vertical y-axis intersect.

Analyze the shaded regions

Using the Systems of Linear Inequalities knowledge point
A system of linear inequalities is represented graphically by overlapping shaded regions. The solution set of the system is the region where all individual shaded regions overlap (the intersection). On this graph, one inequality is shaded blue, another is shaded red, and their intersection is the dark purple/grey region.

Check if the point is in the solution region

Using the Systems of Linear Inequalities knowledge point
Looking at the origin \( (0,0) \):

• It lies on the solid boundary line of the blue region.
• It lies inside the red shaded region.
• However, it is not in the overlapping dark purple/grey region, which represents the solution set of the system.
• Therefore, \( (0,0) \) is not a solution to the system.

Answer:

• Solution
• Not a Solution (Correct answer)