Question

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

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 plus 9 y equals 55 3 x minus 9 y equals negative 15

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

Answer 1

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

1. **System 1:**
\[
7x - 9y = 55
\]
\[
3x - 9y = -15
\]
Substitute \( x = 4 \) and \( y = -3 \):
- For \( 7x - 9y = 55 \):
\[
7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(true)}
\]
- For \( 3x - 9y = -15 \):
\[
3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(false)}
\]

This system does not work.

2. **System 2:**
\[
7x + 9y = 55
\]
\[
3x - 9y = -15
\]
Substitute \( x = 4 \) and \( y = -3 \):
- For \( 7x + 9y = 55 \):
\[
7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(false)}
\]
- For \( 3x - 9y = -15 \):
\[
3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(false)}
\]

This system does not work.

3. **System 3:**
\[
7x + 9y = 55
\]
\[
3x + 9y = -15
\]
Substitute \( x = 4 \) and \( y = -3 \):
- For \( 7x + 9y = 55 \):
\[
7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(false)}
\]
- For \( 3x + 9y = -15 \):
\[
3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(true)}
\]

This system does not work.

4. **System 4:**
\[
7x - 9y = 55
\]
\[
3x + 9y = -15
\]
Substitute \( x = 4 \) and \( y = -3 \):
- For \( 7x - 9y = 55 \):
\[
7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(true)}
\]
- For \( 3x + 9y = -15 \):
\[
3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(true)}
\]

Therefore, the correct system of equations for which \( (4, -3) \) is a solution is:
\[
7x - 9y = 55 \quad \text{and} \quad 3x + 9y = -15.
\]

This means the answer is **System 4: \( 7x - 9y = 55 \) and \( 3x + 9y = -15 \).**