Question

(4,−3) is the correct solution to which system?

7x+9y=55
3x+ 9y=−15

7x−9y=55
3x− 9y=−15

7x+9y=55
3x−9y=−15

7x−9y=55
3x+ 9y=−15

Answer 1

To determine which system has (4, -3) as a solution, we can plug the values \(x = 4\) and \(y = -3\) into each equation in the systems provided.

### System 1:
1. \(7x + 9y = 55\)
- Substitute \(x = 4\) and \(y = -3\):
\[
7(4) + 9(-3) = 28 - 27 = 1 \quad (\text{not } 55)
\]

2. \(3x + 9y = -15\)
- Substitute \(x = 4\) and \(y = -3\):
\[
3(4) + 9(-3) = 12 - 27 = -15 \quad (\text{true})
\]

### System 2:
1. \(7x - 9y = 55\)
- Substitute \(x = 4\) and \(y = -3\):
\[
7(4) - 9(-3) = 28 + 27 = 55 \quad (\text{true})
\]

2. \(3x - 9y = -15\)
- Substitute \(x = 4\) and \(y = -3\):
\[
3(4) - 9(-3) = 12 + 27 = 39 \quad (\text{not } -15)
\]

### System 3:
1. \(7x + 9y = 55\)
- Substitute \(x = 4\) and \(y = -3\):
\[
7(4) + 9(-3) = 28 - 27 = 1 \quad (\text{not } 55)
\]

2. \(3x - 9y = -15\)
- Substitute \(x = 4\) and \(y = -3\):
\[
3(4) - 9(-3) = 12 + 27 = 39 \quad (\text{not } -15)
\]

### System 4:
1. \(7x - 9y = 55\)
- Substitute \(x = 4\) and \(y = -3\):
\[
7(4) - 9(-3) = 28 + 27 = 55 \quad (\text{true})
\]

2. \(3x + 9y = -15\)
- Substitute \(x = 4\) and \(y = -3\):
\[
3(4) + 9(-3) = 12 - 27 = -15 \quad (\text{true})
\]

### Conclusion:
(4, -3) is the correct solution to **System 4**:
\[
7x - 9y = 55
\]
\[
3x + 9y = -15
\]