Question

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

(1 point)
Responses

-5x + y = -2

-3x + 6y = -12

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

-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 - 3

3x - 8y = 24

Answer 1

To determine which system the point (0, -2) is a solution for, we need to substitute \(x = 0\) and \(y = -2\) into each equation in each given system.

Let's check each option:

1. **For the system:**
- \(-5x + y = -2\)
- \(-3x + 6y = -12\)

Substituting \(x = 0\) and \(y = -2\):
- For \(-5(0) + (-2) = -2\) → \(-2 = -2\) (True)
- For \(-3(0) + 6(-2) = -12\) → \(0 - 12 = -12\) (True)

So, (0, -2) is a solution for this system.

2. **For the system:**
- \(-4x + y = 6\)
- \(-5x - y = 21\)

Substituting:
- For \(-4(0) + (-2) = 6\) → \(-2 = 6\) (False)

Not a solution.

3. **For the system:**
- \(x + y = 2\)
- \(-x + 2y = 16\)

Substituting:
- For \(0 + (-2) = 2\) → \(-2 = 2\) (False)

Not a solution.

4. **For the system:**
- \(-5x = y - 3\)
- \(3x - 8y = 24\)

Substituting:
- For \(-5(0) = -2 - 3\) → \(0 = -5\) (False)

Not a solution.

Based on the checks, the point (0, -2) is a solution to the first system:

\(-5x + y = -2\) and \(-3x + 6y = -12\).