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To determine which point would *not* be a solution to the given system of inequalities, let’s examine each inequality with the provided points:

### Inequalities:
1. \( y \geq \frac{3}{2}x + 4 \)
2. \( y < \frac{1}{2}x + 5 \)

For each point, we will substitute the \( x \) and \( y \) values and check if they satisfy both inequalities.

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### Testing the Points:

1. **Point \((-8, -4)\):**
   - **First inequality:** \( -4 \geq \frac{3}{2}(-8) + 4 \Rightarrow -4 \geq -12 + 4 \Rightarrow -4 \geq -8\) (True)
   - **Second inequality:** \( -4 < \frac{1}{2}(-8) + 5 \Rightarrow -4 < -4 + 5 \Rightarrow -4 < 1\) (True)
   
   This point satisfies both inequalities.

2. **Point \((-8, -2)\):**
   - **First inequality:** \( -2 \geq \frac{3}{2}(-8) + 4 \Rightarrow -2 \geq -12 + 4 \Rightarrow -2 \geq -8\) (True)
   - **Second inequality:** \( -2 < \frac{1}{2}(-8) + 5 \Rightarrow -2 < -4 + 5 \Rightarrow -2 < 1\) (True)
   
   This point satisfies both inequalities.

3. **Point \((-12, -6)\):**
   - **First inequality:** \( -6 \geq \frac{3}{2}(-12) + 4 \Rightarrow -6 \geq -18 + 4 \Rightarrow -6 \geq -14\) (True)
   - **Second inequality:** \( -6 < \frac{1}{2}(-12) + 5 \Rightarrow -6 < -6 + 5 \Rightarrow -6 < -1\) (True)
   
   This point satisfies both inequalities.

4. **Point \((8, 0)\):**
   - **First inequality:** \( 0 \geq \frac{3}{2}(8) + 4 \Rightarrow 0 \geq 12 + 4 \Rightarrow 0 \geq 16\) (False)
   
   Since this point does not satisfy the first inequality, it does not satisfy the system.

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### Conclusion:
The point \((8, 0)\) **would not** be a solution to the system of inequalities.

Would you like further details on this solution, or do you have any additional questions?

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### Related Questions:
1. How do you determine if a point is a solution to a system of inequalities?
2. What are common strategies for solving systems of linear inequalities graphically?
3. How do you graph inequalities with different inequality symbols (e.g., \( \geq \) vs. \( > \))?
4. What applications do systems of inequalities have in real-life situations?
5. How can we interpret the intersection region of inequalities?

### Tip:
When testing points in a system of inequalities, always substitute each point into each inequality and verify if the point satisfies all inequalities in the system.

Which point would not be a solution to the system of linear inequalities shown below? y ≥ (3/2)x + 4 and y < (1/2)x + 5

Learn how to identify which points do not satisfy a system of linear inequalities with a step-by-step solution. This example includes the inequalities y ≥ (3/2)x + 4 and y < (1/2)x + 5, perfect for students in Grades 9-10.

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