Is (6,3) a solution to this system of inequalities? 7x+17y>-1 and x>-5 yes or no?

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.

Learn how to determine if the point (6, 3) satisfies the system of inequalities 7x + 17y > -1 and x > -5 with a step-by-step explanation. This example covers algebraic concepts and coordinate geometry, suitable for students in Grades 6-8.

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