Algebra-1

Question Analysis
This question involves determining whether the point  lies within the solution region of a system of linear inequalities using a graphical approach.

Key Concept Explanation
When analyzing a system of linear inequalities graphically:
Each inequality corresponds to a half-plane, bounded by a boundary line.
A solid boundary line is used for inequalities with  or  (including the line itself), while a dashed line is used for > or < (excluding the line).
The solution region of the system is the intersection (overlap) of the half-planes defined by each inequality.
A point is in the solution region if it lies within this overlap.

Step-by-step Solution
1. Graph the first inequality 
Boundary line:  (a straight line with a slope of 4 and a y-intercept of ).
Since the inequality is , the line is solid (inclusive of the line).
Shaded region: Use a test point (e.g., ) to determine the shaded side.
Substituting into the inequality:  simplifies to , which is false.
Thus, we shade the half-plane below the line (the opposite side of the test point).
2. Graph the second inequality y > -x + 5
Boundary line:  (a straight line with a slope of  and a y-intercept of 5).
Since the inequality is >, the line is dashed (exclusive of the line).
Shaded region: Use the test point  again.
Substituting: 0 > -(0) + 5 simplifies to 0 > 5, which is false.
Thus, we shade the half-plane above the line (the opposite side of the test point).
3. Identify the solution region
The solution region is the overlap of the two shaded half-planes from the first and second inequalities.
4. Check if  is in the solution region
Locate the point  on the graph:
For the first inequality: The point lies below the solid line 

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