Is it possible to change the inequality symbol(s) so that one, but not both of the points is a solution of the system? Explain.

This isis not possible. If one inequality symbol changes bothneither become(s) a solution.  If both inequality symbols change bothneither become(s) a solution.

The question asks whether it's possible to change the inequality symbols in a system of inequalities such that exactly one, but not both, of the points becomes a solution.

### Explanation:

1. **Changing One Inequality Symbol:**
   - If you change the inequality symbol for one of the inequalities (e.g., from \( \leq \) to \( > \)), you might exclude a certain region that was previously part of the solution set. However, this change can either make both points cease to be solutions or make both points still satisfy the other inequality.

2. **Changing Both Inequality Symbols:**
   - If both inequality symbols are changed, you may reverse the solution regions entirely. This would typically mean that neither of the original points would be solutions anymore, or both might still satisfy the newly defined regions.

### Conclusion:

- The statement in your message is **correct**. If you change one inequality, either both points still satisfy one of the inequalities or neither does. Changing both inequality symbols might result in neither of the points being solutions. Thus, it's not possible to adjust the inequalities so that only one point is a solution without affecting the other in a predictable way.

Would you like to explore this concept with specific examples or further clarifications?

### 5 Related Questions:
1. What happens if you reverse the inequality signs in a system of inequalities?
2. How do boundary conditions affect the solutions of inequalities?
3. Can a system of inequalities have exactly one solution?
4. What is the graphical interpretation of a system of inequalities?
5. How do inequalities change when you multiply or divide by a negative number?

### Tip:
When working with inequalities, always check the solution set by plugging in test points to ensure your understanding of the regions they represent.

Explore whether changing inequality symbols in a system of inequalities can affect the solutions. Understand the implications of altering inequality signs and how it impacts the solution sets.

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