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To determine which ordered pair is in the solution set of the given system of inequalities, we need to test each ordered pair against the two inequalities:

**Inequalities:**
1. \( y < \frac{1}{2}x + 4 \)
2. \( y \geq -x + 1 \)

Let's test each option:

### A. \((-5, 3)\)

1. Check \( y < \frac{1}{2}x + 4 \):
   \[
   3 < \frac{1}{2}(-5) + 4 = -2.5 + 4 = 1.5 \quad (\text{False})
   \]

Since the first inequality is false, this pair does not satisfy the system.

### B. \((0, 4)\)

1. Check \( y < \frac{1}{2}x + 4 \):
   \[
   4 < \frac{1}{2}(0) + 4 = 4 \quad (\text{False})
   \]
   
Since the first inequality is false, this pair does not satisfy the system.

### C. \((3, -5)\)

1. Check \( y < \frac{1}{2}x + 4 \):
   \[
   -5 < \frac{1}{2}(3) + 4 = 1.5 + 4 = 5.5 \quad (\text{True})
   \]

2. Check \( y \geq -x + 1 \):
   \[
   -5 \geq -(3) + 1 = -3 + 1 = -2 \quad (\text{False})
   \]

Since the second inequality is false, this pair does not satisfy the system.

### D. \((4, 0)\)

1. Check \( y < \frac{1}{2}x + 4 \):
   \[
   0 < \frac{1}{2}(4) + 4 = 2 + 4 = 6 \quad (\text{True})
   \]

2. Check \( y \geq -x + 1 \):
   \[
   0 \geq -(4) + 1 = -4 + 1 = -3 \quad (\text{True})
   \]

Since both inequalities are true for this pair, the correct answer is:

**Answer: D. (4, 0)**

Would you like further details or explanations?

### Related Questions:
1. How do you graph a system of inequalities?
2. What does the solution set of a system of inequalities represent?
3. How can you determine if a point lies within the solution set of an inequality?
4. What strategies can be used to solve systems of linear inequalities?
5. What are the real-world applications of systems of inequalities?

**Tip:** Always check each point in the system of inequalities separately to ensure it satisfies all conditions.

Which ordered pair is in the solution set of the following system of inequalities?

y < 1/2x + 4
y ≥ -x + 1

A. (-5, 3)
B. (0, 4)
C. (3, -5)
D. (4, 0)

Learn how to determine which ordered pair is part of the solution set for a system of inequalities. This problem involves graphing and analyzing inequalities, suitable for Grades 9-12. Step-by-step guide provided.

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