Is (5,-4) a solution to this system of inequalities? 17x+17y<18 and 15x+14y>20 yes or no

To determine whether \((5, -4)\) is a solution to the system of inequalities:

1. **First inequality**: \( 17x + 17y < 18 \)
   - Substitute \(x = 5\) and \(y = -4\):
   \[
   17(5) + 17(-4) = 85 - 68 = 17
   \]
   Since \(17 < 18\), the point satisfies the first inequality.

2. **Second inequality**: \( 15x + 14y > 20 \)
   - Substitute \(x = 5\) and \(y = -4\):
   \[
   15(5) + 14(-4) = 75 - 56 = 19
   \]
   Since \(19 \not> 20\), the point does **not** satisfy the second inequality.

Thus, the point \((5, -4)\) is **not** a solution to the system of inequalities.

Would you like more details on the reasoning? Here are 5 related questions:

1. How do you determine if a point satisfies a system of inequalities?
2. Can systems of inequalities have more than one solution?
3. What happens when a point satisfies only one inequality in a system?
4. How do graphical methods help in solving systems of inequalities?
5. Can you solve systems of inequalities algebraically like systems of equations?

**Tip**: Always substitute each variable into the inequalities to check if both conditions hold.

Determine whether the point (5, -4) is a solution to the system of inequalities 17x + 17y < 18 and 15x + 14y > 20. This problem involves substitution into inequalities and is suitable for students in Grades 9-10.

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