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.