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To solve this problem, we need to check whether each ordered pair \((x, y)\) satisfies the equation \(2x - 7y = -11\). For each ordered pair, we will substitute the values of \(x\) and \(y\) into the equation and check if the left-hand side equals the right-hand side (-11). 

Let's go through the process for each pair:

1. **For \((-3, 4)\):**
   \[
   2(-3) - 7(4) = -6 - 28 = -34 \quad (\text{not equal to } -11)
   \]
   Therefore, \((-3, 4)\) is **not** a solution.

2. **For \((8, -2)\):**
   \[
   2(8) - 7(-2) = 16 + 14 = 30 \quad (\text{not equal to } -11)
   \]
   Therefore, \((8, -2)\) is **not** a solution.

3. **For \((5, 3)\):**
   \[
   2(5) - 7(3) = 10 - 21 = -11 \quad (\text{equals } -11)
   \]
   Therefore, \((5, 3)\) is a **solution**.

4. **For \((-1, -5)\):**
   \[
   2(-1) - 7(-5) = -2 + 35 = 33 \quad (\text{not equal to } -11)
   \]
   Therefore, \((-1, -5)\) is **not** a solution.

### Summary:
- \((-3, 4)\): No
- \((8, -2)\): No
- \((5, 3)\): Yes
- \((-1, -5)\): No

Would you like any further details or clarification?

### Related Questions:
1. What does it mean for an ordered pair to be a solution to a linear equation?
2. How do we graphically interpret the solutions to the equation \(2x - 7y = -11\)?
3. How can we determine the solution to a linear equation without testing multiple points?
4. What are some methods to solve a system of linear equations algebraically?
5. How would you solve the equation if additional pairs were provided?

### Tip:
Always substitute the values of \(x\) and \(y\) carefully into the equation to ensure accuracy when checking for solutions.

For each ordered pair, determine whether it is a solution to 2x - 7y = -11.

Check whether each ordered pair (x, y) is a solution to the linear equation 2x - 7y = -11. Learn step-by-step how to substitute and verify if the pair satisfies the equation. Suitable for students in Grades 8-10.

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