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

\[
\begin{aligned}
-5x + 4y &= 2 \\
3x - 5y &= 4
\end{aligned}
\]

we need to substitute each ordered pair \((x, y)\) into both equations and check if both equations hold true. 

Let's check each one:

### 1. Ordered pair \((6, 8)\)
Substitute \(x = 6\) and \(y = 8\) into both equations:
- First equation: 
\[
-5(6) + 4(8) = -30 + 32 = 2 \quad \text{(True)}
\]
- Second equation:
\[
3(6) - 5(8) = 18 - 40 = -22 \quad \text{(False)}
\]
Since the second equation is false, \((6, 8)\) is **not a solution**.

### 2. Ordered pair \((3, 1)\)
Substitute \(x = 3\) and \(y = 1\):
- First equation: 
\[
-5(3) + 4(1) = -15 + 4 = -11 \quad \text{(False)}
\]
- Second equation:
\[
3(3) - 5(1) = 9 - 5 = 4 \quad \text{(True)}
\]
Since the first equation is false, \((3, 1)\) is **not a solution**.

### 3. Ordered pair \((-7, 0)\)
Substitute \(x = -7\) and \(y = 0\):
- First equation: 
\[
-5(-7) + 4(0) = 35 + 0 = 35 \quad \text{(False)}
\]
- Second equation:
\[
3(-7) - 5(0) = -21 + 0 = -21 \quad \text{(False)}
\]
Both equations are false, so \((-7, 0)\) is **not a solution**.

### 4. Ordered pair \((-4, -4)\)
Substitute \(x = -4\) and \(y = -4\):
- First equation: 
\[
-5(-4) + 4(-4) = 20 - 16 = 4 \quad \text{(False)}
\]
- Second equation:
\[
3(-4) - 5(-4) = -12 + 20 = 8 \quad \text{(False)}
\]
Both equations are false, so \((-4, -4)\) is **not a solution**.

### Conclusion:
- \((6, 8)\) is **not a solution**.
- \((3, 1)\) is **not a solution**.
- \((-7, 0)\) is **not a solution**.
- \((-4, -4)\) is **not a solution**.

Would you like any further details or explanations?

### Relative Questions:
1. How can we determine the solution to a system of equations graphically?
2. What methods can be used to solve systems of equations algebraically (e.g., substitution, elimination)?
3. What is the determinant of a system of linear equations, and how does it relate to solutions?
4. How do systems of linear equations apply in real-world contexts?
5. What does it mean when a system of equations has no solution or infinitely many solutions?

### Tip:
Always check both equations in a system when testing whether an ordered pair is a solution.

For each ordered pair, determine whether it is a solution to the system of equations:
-5x + 4y = 2
3x - 5y = 4
(6, 8), (3, 1), (-7, 0), (-4, -4)

Solve a system of linear equations with ordered pairs (6, 8), (3, 1), (-7, 0), and (-4, -4) by substituting values into the equations -5x + 4y = 2 and 3x - 5y = 4. This solution covers key algebraic concepts for students in Grades 8-10.

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