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The problem asks to identify the system of inequalities that models the election of new board members for a debate club, with the following constraints:

1. The total number of board members from the junior (\(j\)) and senior (\(s\)) classes must be between 4 and 7 members.
2. There must be at least 2 juniors (\(j \geq 2\)).
3. There must be at least 2 seniors (\(s \geq 2\)).

Let's analyze the answer options:

- **Option A:** \( 4 \leq j - s \leq 7, j \geq 2, s \geq 2 \)
  - This is incorrect because it involves the difference between \(j\) and \(s\) (\(j - s\)), while we need the total number of juniors and seniors together.

- **Option B:** \( 0 \leq j - s \leq 7, j \geq 2, s \geq 2 \)
  - This is also incorrect for the same reason as Option A: it focuses on the difference between juniors and seniors rather than the sum.

- **Option C:** \( 4 \leq j + s \leq 7, j \geq 2, s \geq 2 \)
  - This is correct because it properly models the total number of board members (\( j + s \)) as being between 4 and 7, while ensuring that there are at least 2 juniors and 2 seniors.

- **Option D:** \( 0 \leq j + s \leq 7, j \geq 2, s \geq 2 \)
  - This is incorrect because it allows the total number of board members to be as low as 0, which contradicts the problem's requirement of at least 4 members.

Thus, the correct answer is **Option C**.

Would you like more details on this solution or have any further questions?

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Here are 5 related questions for practice:
1. How would the system of inequalities change if there had to be at least 3 juniors?
2. What if the total number of board members had to be between 5 and 9 instead?
3. How would the system look if there were no minimum requirement for juniors and seniors?
4. Can you represent this scenario graphically on the coordinate plane?
5. What if the juniors must be at least half of the total board members?

**Tip:** When modeling real-world scenarios with inequalities, always make sure that each part of the problem is translated accurately into the system.

The Debate Club at a local high school is electing its new board positions. It must have 4 to 7 new board members from the junior (j) and senior (s) classes. The board must include at least 2 juniors and at least 2 seniors. Which of the following systems models this scenario?

Understand how to model inequalities for a high school debate club's board election, with a system of inequalities that ensures 4-7 members, including at least 2 juniors and 2 seniors. Perfect for algebra practice for students in Grades 7-10.

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