Question

Remember: You can use your graphing calculator!

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

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
Skip to navigation

Answer 1

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

### Checking the first system:
1. **First equation:**
\[
-5(0) + (-2) = -2 \quad \Rightarrow \quad -2 = -2 \quad \text{(True)}
\]

2. **Second equation:**
\[
-3(0) + 6(-2) = -12 \quad \Rightarrow \quad 0 - 12 = -12 \quad \Rightarrow \quad -12 = -12 \quad \text{(True)}
\]

Both equations are satisfied, so (0, -2) is a solution to the first system.

### Checking the second system:
1. **First equation:**
\[
(0) + (-2) = 2 \quad \Rightarrow \quad -2 = 2 \quad \text{(False)}
\]

Since the first equation is not true, (0, -2) is not a solution for the second system.

### Checking the third system:
1. **First equation:**
\[
-4(0) + (-2) = 6 \quad \Rightarrow \quad -2 = 6 \quad \text{(False)}
\]

Since the first equation is not true, (0, -2) is not a solution for the third system.

### Checking the fourth system:
1. **First equation:**
\[
-5(0) = -2 - 3 \quad \Rightarrow \quad 0 = -5 \quad \text{(False)}
\]

Since the first equation is not true, (0, -2) is not a solution for the fourth system.

### Conclusion:
The point (0, -2) is a solution to the system:
\[
\begin{align*}
-5x + y &= -2 \\
-3x + 6y &= -12
\end{align*}
\]