Question

(4,−3)
is the correct solution to which system?(1 point)
Responses

7x+9y=55

3x+ 9y=−15
7 x plus 9 y equals 55 3 x plus 9 y equals negative 15

7x−9y=55

3x− 9y=−15
7 x minus 9 y equals 55 3 x minus 9 y equals negative 15

7x−9y=55

3x+ 9y=−15
7 x minus 9 y equals 55 3 x plus 9 y equals negative 15

7x+9y=55

3x−9y=−15

Answer 1

To find the correct system of equations for which \((4, -3)\) is the solution, we need to substitute \(x = 4\) and \(y = -3\) into each system of equations and check which one satisfies both equations.

### System 1:
1. \(7x + 9y = 55\)
\[
7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(not satisfied)}
\]
2. \(3x + 9y = -15\)
\[
3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(satisfied)}
\]

### System 2:
1. \(7x - 9y = 55\)
\[
7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(satisfied)}
\]
2. \(3x - 9y = -15\)
\[
3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(not satisfied)}
\]

### System 3:
1. \(7x - 9y = 55\)
\[
7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(satisfied)}
\]
2. \(3x + 9y = -15\)
\[
3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(satisfied)}
\]

### System 4:
1. \(7x + 9y = 55\)
\[
7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(not satisfied)}
\]
2. \(3x - 9y = -15\)
\[
3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(not satisfied)}
\]

### Conclusion:
The correct system of equations is:
- \(7x - 9y = 55\)
- \(3x + 9y = -15\)

So the answer is:
**7x−9y=55 and 3x+9y=−15.**