Question

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

(1 point)
Responses

x + y = 2

-x + 2y = 16

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

-5x = y - 3

3x - 8y = 24

-5x = y - 3 3x - 8y = 24

-5x + y = -2

-3x + 6y = -12

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

-4x + y = 6

-5x - y = 21

Answer 1

To determine which system of equations the point (0, -2) is a solution to, we substitute x = 0 and y = -2 into each equation of the systems provided.

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

Substituting (0, -2):
- \( 0 + (-2) = 2 \) → \( -2 = 2 \) (not true)
- \( -0 + 2(-2) = 16 \) → \( -4 = 16 \) (not true)

This system does not work.

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

This is the same as above.

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

Substituting (0, -2):
- \( -5(0) = -2 - 3 \) → \( 0 = -5 \) (not true)
- \( 3(0) - 8(-2) = 24 \) → \( 0 + 16 = 24 \) (not true)

This system does not work.

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

Substituting (0, -2):
- \( -5(0) - 2 = -2 \) → \( 0 - 2 = -2 \) (true)
- \( -3(0) + 6(-2) = -12 \) → \( 0 - 12 = -12 \) (true)

This system works!

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

Substituting (0, -2):
- \( -4(0) - 2 = 6 \) → \( 0 - 2 = 6 \) (not true)
- \( -5(0) - (-2) = 21 \) → \( 0 + 2 = 21 \) (not true)

This system does not work.

Therefore, the point (0, -2) is a solution to the system:
**-5x + y = -2 and -3x + 6y = -12.**