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

7x+9y=55

3x+ 9y=−15

Answer 1

To determine which system has the correct solution (4, -3), we can substitute x = 4 and y = -3 into each system of equations and check if both equations hold true.

Let's evaluate each system one by one:

**1. System:**
- \( 7x + 9y = 55 \)
- \( 3x - 9y = -15 \)

Substituting \( x = 4 \) and \( y = -3 \):

- For \( 7x + 9y \):
\[
7(4) + 9(-3) = 28 - 27 = 1 \neq 55
\]
(Does not hold)

- For \( 3x - 9y \):
\[
3(4) - 9(-3) = 12 + 27 = 39 \neq -15
\]
(Does not hold)

---

**2. System:**
- \( 7x - 9y = 55 \)
- \( 3x + 9y = -15 \)

Substituting \( x = 4 \) and \( y = -3 \):

- For \( 7x - 9y \):
\[
7(4) - 9(-3) = 28 + 27 = 55
\]
(Holds)

- For \( 3x + 9y \):
\[
3(4) + 9(-3) = 12 - 27 = -15
\]
(Holds)

---

**3. System:**
- \( 7x - 9y = 55 \)
- \( 3x - 9y = -15 \)

Substituting \( x = 4 \) and \( y = -3 \):

- For \( 7x - 9y \):
\[
7(4) - 9(-3) = 28 + 27 = 55
\]
(Holds)

- For \( 3x - 9y \):
\[
3(4) - 9(-3) = 12 + 27 = 39 \neq -15
\]
(Does not hold)

---

**4. System:**
- \( 7x + 9y = 55 \)
- \( 3x + 9y = -15 \)

Substituting \( x = 4 \) and \( y = -3 \):

- For \( 7x + 9y \):
\[
7(4) + 9(-3) = 28 - 27 = 1 \neq 55
\]
(Does not hold)

- For \( 3x + 9y \):
\[
3(4) + 9(-3) = 12 - 27 = -15
\]
(Holds)

---

Based on this evaluation, the correct system is the **second system**:

- \( 7x - 9y = 55 \)
- \( 3x + 9y = -15 \)