Question

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

7z-9y=55
O

O

3z-9y =- 15

7z+9y=55
3z + 9y =- 15

7z+9y=55
3z-9y =- 15

7z-9y=55
3z + 9y =- 15

Answer 1

To determine which system of equations has the point (4, -3) as a solution, we will plug in \( z = 4 \) and \( y = -3 \) into each equation of the given options.

1. **First system:**
- \( 7z - 9y = 55 \)
\[
7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(True)}
\]
- \( 3z - 9y = -15 \)
\[
3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(False)}
\]

2. **Second system:**
- \( 7z + 9y = 55 \)
\[
7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(False)}
\]
- \( 3z + 9y = -15 \)
\[
3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(True)}
\]

3. **Third system:**
- \( 7z + 9y = 55 \)
\[
7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(False)}
\]
- \( 3z - 9y = -15 \)
\[
3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(False)}
\]

4. **Fourth system:**
- \( 7z - 9y = 55 \)
\[
7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(True)}
\]
- \( 3z + 9y = -15 \)
\[
3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(True)}
\]

The fourth system, which consists of the equations \( 7z - 9y = 55 \) and \( 3z + 9y = -15 \), is satisfied by \( (4, -3) \).

So the answer is:

**7z - 9y = 55 and 3z + 9y = -15**.