Algebra-1

Question Analysis
This question involves a system of linear inequalities and requires determining if a given point  lies within the solution region of the system.
The solution region of a system of inequalities is the set of all points that satisfy all inequalities in the system simultaneously.

Key Concept Explanation
To analyze the solution region of a system of linear inequalities graphically:
Each inequality corresponds to a half - plane (a region on one side of a boundary line).
The boundary line of an inequality  is solid if the inequality includes equality ( or ) and dashed if it does not (> or <).
The solution region of the system is the intersection (overlap) of the half - planes defined by each inequality.
A point lies in the solution region if it is within this overlapping area.

Step-by-step Solution
1. Graph the first inequality 
Boundary line:  (a straight line with a slope of 2 and a y - intercept of ). Since the inequality is , the line is solid (inclusive of the line itself).
Shaded region: To find which side of the line to shade, use a test point (e.g., ). Substituting into the inequality:  simplifies to , which is true.
So, we shade the half - plane above the line  (including the line).
2. Graph the second inequality 
Boundary line: 

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