Question

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The point (0,-2) is a solution to which system?

(1 point)
Responses

-4x + y = 6

-5x - y = 21

-4x + y = 6 -5x - y = 21

-5x + y = -2

-3x + 6y = -12

-5x + y = -2 -3x + 6y = -12

x + y = 2

-x + 2y = 16

x + y = 2 -x + 2y = 16

-5x = y - 3

3x - 8y = 24

Answer 1

To check if the point (0, -2) is a solution to a given system of equations, we can substitute \( x = 0 \) and \( y = -2 \) into each equation in the provided systems.

1. **System:**
- \( -4x + y = 6 \)
- \( -5x - y = 21 \)

Checking \( -4(0) + (-2) = 6 \) → \(-2 \neq 6\) (not a solution)

Checking \( -5(0) - (-2) = 21 \) → \(2 \neq 21\) (not a solution)

**Conclusion:** (0, -2) is NOT a solution for this system.

2. **System:**
- \( -5x + y = -2 \)
- \( -3x + 6y = -12 \)

Checking \( -5(0) + (-2) = -2 \) → \(-2 = -2\) (a solution)

Checking \( -3(0) + 6(-2) = -12 \) → \(-12 = -12\) (a solution)

**Conclusion:** (0, -2) is a solution for this system.

3. **System:**
- \( x + y = 2 \)
- \( -x + 2y = 16 \)

Checking \( 0 + (-2) = 2 \) → \(-2 \neq 2\) (not a solution)

Checking \( -0 + 2(-2) = 16 \) → \(-4 \neq 16\) (not a solution)

**Conclusion:** (0, -2) is NOT a solution for this system.

4. **System:**
- \( -5x = y - 3 \)
- \( 3x - 8y = 24 \)

Checking \( -5(0) = -2 - 3 \) → \(0 = -5\) (not a solution)

Checking \( 3(0) - 8(-2) = 24 \) → \(16 \neq 24\) (not a solution)

**Conclusion:** (0, -2) is NOT a solution for this system.

### Final Answer:
The point (0, -2) is a solution to the system:
- **\( -5x + y = -2 \)**
- **\( -3x + 6y = -12 \)**.