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

-4x + y = 6

-5x - y = 21

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

-5x + y = -2

-3x + 6y = -12

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

Answer 1

To determine which system has the point (0, -2) as a solution, we need to substitute \(x = 0\) and \(y = -2\) into each equation of the given systems and see which one holds true.

**System 1:**
1. \(x + y = 2\)
- \(0 + (-2) = 2\)
- \(-2 \neq 2\) (Not a solution)

2. \(-x + 2y = 16\)
- \(-0 + 2(-2) = 16\)
- \(-4 \neq 16\) (Not a solution)

So, **(0, -2)** is not a solution to this system.

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**System 2:**
1. \(-5x = y - 3\)
- \(-5(0) = -2 - 3\)
- \(0 = -5\) (Not a solution)

2. \(3x - 8y = 24\)
- \(3(0) - 8(-2) = 24\)
- \(16 \neq 24\) (Not a solution)

So, **(0, -2)** is not a solution to this system as well.

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**System 3:**
1. \(-4x + y = 6\)
- \(-4(0) + (-2) = 6\)
- \(-2 \neq 6\) (Not a solution)

2. \(-5x - y = 21\)
- \(-5(0) - (-2) = 21\)
- \(2 \neq 21\) (Not a solution)

So, **(0, -2)** is not a solution to this system either.

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**System 4:**
1. \(-5x + y = -2\)
- \(-5(0) + (-2) = -2\)
- \(-2 = -2\) (True, it is a solution)

2. \(-3x + 6y = -12\)
- \(-3(0) + 6(-2) = -12\)
- \(-12 = -12\) (True, it is a solution)

**(0, -2)** is a solution to **this system.**

Therefore, the correct system is:
**-5x + y = -2, -3x + 6y = -12.**