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To determine whether each ordered pair is a solution to the system of equations given:

\[
6x - 7y = 4
\]
\[
-5x + 3y = 8
\]

we'll substitute each pair \((x, y)\) into both equations and check if both equations are satisfied.

### Ordered Pair (-4, -4)

1. Substitute into \(6x - 7y = 4\):
   \[
   6(-4) - 7(-4) = -24 + 28 = 4
   \]
   True.

2. Substitute into \(-5x + 3y = 8\):
   \[
   -5(-4) + 3(-4) = 20 - 12 = 8
   \]
   True.

**(-4, -4) is a solution.**

---

### Ordered Pair (3, 2)

1. Substitute into \(6x - 7y = 4\):
   \[
   6(3) - 7(2) = 18 - 14 = 4
   \]
   True.

2. Substitute into \(-5x + 3y = 8\):
   \[
   -5(3) + 3(2) = -15 + 6 = -9
   \]
   False.

**(3, 2) is not a solution.**

---

### Ordered Pair (-1, 1)

1. Substitute into \(6x - 7y = 4\):
   \[
   6(-1) - 7(1) = -6 - 7 = -13
   \]
   False.

**(-1, 1) is not a solution.**

---

### Ordered Pair (5, 0)

1. Substitute into \(6x - 7y = 4\):
   \[
   6(5) - 7(0) = 30 - 0 = 30
   \]
   False.

**(5, 0) is not a solution.**

---

### Summary Table:

| (x, y)   | Is it a solution? |
|----------|--------------------|
| (-4, -4) | Yes               |
| (3, 2)   | No                |
| (-1, 1)  | No                |
| (5, 0)   | No                |

Would you like further details or have any questions?

Here are some related questions:
1. How would the solution change if the second equation were different?
2. Can substitution or elimination methods confirm these results?
3. What other pairs might satisfy this system of equations?
4. How can you tell if a system of equations has no solution, one solution, or infinitely many solutions?
5. Why is it necessary to check both equations to confirm a solution?

**Tip:** Always verify both equations when checking solutions to a system.

For each ordered pair, determine whether it is a solution to the system of equations:
6x - 7y = 4
-5x + 3y = 8

Find out if each ordered pair is a solution to the given system of linear equations. This exercise involves substitution and verification, covering essential algebraic concepts suitable for students in Grades 8-10.

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