Question

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

(2 points)
Responses

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

-x+y=2 -x+2y=16
-4x+y=6

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

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

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

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

Answer 1

To determine which system of equations the point \((0, -2)\) is a solution to, we will substitute \(x = 0\) and \(y = -2\) into each set of equations and verify if both equations in that system are satisfied.

1. **System 1:**
- \(-x + y = 2\)
\[
-0 + (-2) = -2 \quad \text{(not satisfied)}
\]
- \(-x + 2y = 16\)
\[
-0 + 2(-2) = -4 \quad \text{(not satisfied)}
\]

This system does not contain the point.

2. **System 2:**
- \(-5x - y = 21\)
\[
-5(0) - (-2) = 2 \quad \text{(not satisfied)}
\]
- \(-4x + y = 6\)
\[
-4(0) + (-2) = -2 \quad \text{(not satisfied)}
\]

This system does not contain the point.

3. **System 3:**
- \(-5x = y - 3\)
\[
-5(0) = -2 - 3 \implies 0 = -5 \quad \text{(not satisfied)}
\]
- \(3x - 8y = 24\)
\[
3(0) - 8(-2) = 16 \quad \text{(not satisfied)}
\]

This system does not contain the point.

4. **System 4:**
- \(-5x + y = -2\)
\[
-5(0) + (-2) = -2 \quad \text{(satisfied)}
\]
- \(-3x + 6y = -12\)
\[
-3(0) + 6(-2) = -12 \quad \text{(satisfied)}
\]

This system does contain the point.

Thus, the correct system of equations that includes the point \((0, -2)\) is:

\[
-5x + y = -2
\]
\[
-3x + 6y = -12
\]

So, the answer is **-5x + y = -2 and -3x + 6y = -12.**