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To solve the given system of inequalities using whole numbers, we will break down the system:

1. \( x + y > 1 \)
2. \( 2x - 3y \leq 7 \)

We will check each of the answer choices by testing the ordered pairs provided to see if they satisfy both inequalities.

### Answer Choices:

1. \( (0, 2), (1, 1) \)
2. \( (0, 2), (1, 1), (2, 1) \)
3. \( (0, 1), (1, 2), (0, 1) \)
4. \( (0, 1), (0, 2), (1, 1), (2, 1) \)

### Step-by-step evaluation:

1. **First inequality**: \( x + y > 1 \)
   - For each pair, we check if the sum of \( x \) and \( y \) is greater than 1.

2. **Second inequality**: \( 2x - 3y \leq 7 \)
   - For each pair, we check if the expression \( 2x - 3y \) is less than or equal to 7.

### Testing the pairs:

1. **(0, 2)**:
   - \( x + y = 0 + 2 = 2 \) (satisfies \( x + y > 1 \))
   - \( 2(0) - 3(2) = -6 \) (satisfies \( 2x - 3y \leq 7 \))
   
2. **(1, 1)**:
   - \( x + y = 1 + 1 = 2 \) (satisfies \( x + y > 1 \))
   - \( 2(1) - 3(1) = -1 \) (satisfies \( 2x - 3y \leq 7 \))

3. **(2, 1)**:
   - \( x + y = 2 + 1 = 3 \) (satisfies \( x + y > 1 \))
   - \( 2(2) - 3(1) = 1 \) (satisfies \( 2x - 3y \leq 7 \))

After testing all the pairs, the answer that satisfies both inequalities is **Option 2: \( (0, 2), (1, 1), (2, 1) \)**.

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

1. What are the methods to graphically represent a system of inequalities?
2. How would you solve this system using substitution or elimination methods?
3. Can systems of inequalities always have integer solutions?
4. What happens if the system of inequalities has no solution?
5. How can you determine the feasibility of solutions in a system like this?

**Tip**: For systems of inequalities, testing boundary points is key to determining feasible regions.

Assume that x and y are whole numbers. Use a table to solve the system of inequalities:
1. x + y > 1
2. 2x - 3y ≤ 7
Choose the correct set of solutions from the options provided.

Learn how to solve a system of inequalities using whole numbers. This example includes x + y > 1 and 2x - 3y ≤ 7. Suitable for students in Grades 6-8, it covers key algebraic concepts and problem-solving strategies.

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