Question

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

x + y = 2

-x + 2y = 16

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

-5x + y = -2

-3x + 6y = -12

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

-5x = y - 3

3x - 8y = 24

Answer 1

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

Let's analyze each system:

1. **System 1:**
- **Equation 1:**
\(-4(0) + (-2) = 6 \rightarrow -2 ≠ 6\) (not true)
- **Equation 2:**
\(-5(0) - (-2) = 21 \rightarrow 2 ≠ 21\) (not true)

This system does not include the point.

2. **System 2:**
- **Equation 1:**
\(0 + (-2) = 2 \rightarrow -2 ≠ 2\) (not true)
- **Equation 2:**
\(-0 + 2(-2) = 16 \rightarrow -4 ≠ 16\) (not true)

This system does not include the point.

3. **System 3:**
- **Equation 1:**
\(-5(0) + (-2) = -2 \rightarrow -2 = -2\) (true)
- **Equation 2:**
\(-3(0) + 6(-2) = -12 \rightarrow -12 = -12\) (true)

This system includes the point.

4. **System 4:**
- **Equation 1:**
\(-5(0) = (-2) - 3 \rightarrow 0 = -5\) (not true)
- **Equation 2:**
\(3(0) - 8(-2) = 24 \rightarrow 16 = 24\) (not true)

This system does not include the point.

After checking all the systems, the only system where the point (0, -2) is a solution is **System 3**:
-5x + y = -2 and -3x + 6y = -12.