To determine if $(6, 3)$ is a solution to the system of inequalities $7x + 17y > -1$ and $x > -5$, we need to check if this point satisfies both inequalities.

1. First inequality: $7x + 17y > -1$ Substituting $x = 6$ and $y = 3$: $7(6) + 17(3) = 42 + 51 = 93$ Since $93 > -1$, the point $(6, 3)$ satisfies the first inequality.

2. Second inequality: $x > -5$ Substituting $x = 6$: $6 > -5$ Since $6 > -5$, the point $(6, 3)$ also satisfies the second inequality.

Since $(6, 3)$ satisfies both inequalities, the answer is yes.

Would you like any more details or have any questions? Here are 5 related questions to consider:

1. How do you graph a system of inequalities?
2. What is the solution set for the system of inequalities?
3. How do you determine if a point lies on the boundary of an inequality?
4. What happens if a point satisfies one inequality but not the other?
5. Can a system of inequalities have more than one solution?

Tip: Always check each inequality separately when determining if a point is a solution to a system of inequalities.