To solve the problem, we need to check which of the given options satisfies the three linear equations provided. We will evaluate each equation with the given coordinates.
### Step-by-Step Solution:
1. **Evaluate the first equation**:
\[
4x + 3y = 24
\]
We will check the coordinates (9, -4) and (3, 4).
- For (9, -4):
\[
4(9) + 3(-4) = 36 - 12 = 24 \quad \text{(True)}
\]
- For (3, 4):
\[
4(3) + 3(4) = 12 + 12 = 24 \quad \text{(True)}
\]
Both coordinates satisfy the first equation.
2. **Evaluate the second equation**:
\[
3x - 4y = 1
\]
We will check the coordinates (-1, 1), (3, 2), and (-3, 2).
- For (-1, 1):
\[
3(-1) - 4(1) = -3 - 4 = -7 \quad \text{(False)}
\]
- For (3, 2):
\[
3(3) - 4(2) = 9 - 8 = 1 \quad \text{(True)}
\]
- For (-3, 2):
\[
3(-3) - 4(2) = -9 - 8 = -17 \quad \text{(False)}
\]
Only (3, 2) satisfies the second equation.
3. **Evaluate the third equation**:
\[
8y - 6x = 4
\]
We will check the coordinate (2, 2).
- For (2, 2):
\[
8(2) - 6(2) = 16 - 12 = 4 \quad \text{(True)}
\]
The coordinate (2, 2) satisfies the third equation.
### Summary of Results:
- The coordinates (9, -4) and (3, 4) satisfy the first equation.
- The coordinate (3, 2) satisfies the second equation.
- The coordinate (2, 2) satisfies the third equation.
### Conclusion:
The solutions for the linear equations are:
- For the first equation: (9, -4) and (3, 4)
- For the second equation: (3, 2)
- For the third equation: (2, 2)
