To determine which point is not a solution to the system of linear inequalities:

1. System of inequalities:

   • $y > x - 8$
   • $y > -x + 8$

2. Approach: Each point must satisfy both inequalities to be a solution. We will substitute each point into both inequalities to see if they satisfy them.

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Evaluate each point:

(12, 5):

• For $y > x - 8$: $5 > 12 - 8$ → $5 > 4$ (True)
• For $y > -x + 8$: $5 > -12 + 8$ → $5 > -4$ (True)
• (12, 5) satisfies both inequalities.

(6, −7):

• For $y > x - 8$: $-7 > 6 - 8$ → $-7 > -2$ (False)
• For $y > -x + 8$: $-7 > -6 + 8$ → $-7 > 2$ (False)
• (6, −7) does not satisfy the inequalities.

(10, 10):

• For $y > x - 8$: $10 > 10 - 8$ → $10 > 2$ (True)
• For $y > -x + 8$: $10 > -10 + 8$ → $10 > -2$ (True)
• (10, 10) satisfies both inequalities.

(10, 8):

• For $y > x - 8$: $8 > 10 - 8$ → $8 > 2$ (True)
• For $y > -x + 8$: $8 > -10 + 8$ → $8 > -2$ (True)
• (10, 8) satisfies both inequalities.

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Conclusion:

The point $(6, -7)$ does not satisfy the system of inequalities, making it the correct answer.

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Would you like a detailed graph of the inequalities or further clarification?

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Related Questions:

1. How can you graphically determine the solution to a system of inequalities?
2. What are the key steps to solving a system of linear inequalities?
3. How does flipping the inequality sign affect solutions when multiplying by negative values?
4. What real-life scenarios can be modeled with linear inequalities?
5. How do boundary lines help in solving linear inequalities?

Tip: When testing points for inequalities, always check each inequality separately to confirm if the point lies in the solution region.