Question

Remember: You can use your graphing calculator!

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

-5x + y = -2

-3x + 6y = -12

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

x + y = 2

-x + 2y = 16

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

-5x = y - 3

3x - 8y = 24

-5x = y - 3 3x - 8y = 24
Skip to navigation



















































page 5 of 5

Answer 1

To determine which system the point (0, -2) is a solution to, we need to check each equation in the given systems by substituting x = 0 and y = -2.

1. **For the first system:**
- **Equation 1:** \(-4x + y = 6\)
- Substitute: \(-4(0) + (-2) = 6 \rightarrow -2 \neq 6\) (not a solution)
- **Equation 2:** \(-5x - y = 21\)
- Substitute: \(-5(0) - (-2) = 21 \rightarrow 2 \neq 21\) (not a solution)

2. **For the second system:**
- **Equation 1:** \(-4x + y = 6\)
- We already found it not to be a solution.
- **Equation 2:** \(-5x + y = -2\)
- Substitute: \(-5(0) + (-2) = -2 \rightarrow -2 = -2\) (is a solution)

3. **For the third system:**
- **Equation 1:** \(-3x + 6y = -12\)
- Substitute: \(-3(0) + 6(-2) = -12 \rightarrow -12 = -12\) (is a solution)
- **Equation 2:** \(-5x + y = -2\)
- We already found this to be true.

4. **For the fourth system:**
- **Equation 1:** \(x + y = 2\)
- Substitute: \(0 + (-2) = 2 \rightarrow -2 \neq 2\) (not a solution)
- **Equation 2:** \(-x + 2y = 16\)
- Substitute: \(-0 + 2(-2) = 16 \rightarrow -4 \neq 16\) (not a solution)

5. **For the fifth system:**
- **Equation 1:** \(-5x = y - 3\)
- Substitute: \(-5(0) = -2 - 3 \rightarrow 0 \neq -5\) (not a solution)
- **Equation 2:** \(3x - 8y = 24\)
- Substitute: \(3(0) - 8(-2) = 24 \rightarrow 16 \neq 24\) (not a solution)

**Conclusion:** Both equations in the second system \(-5x + y = -2\) and \(-3x + 6y = -12\) are true for the point (0, -2). Therefore, the point (0, -2) is a solution to the system:

\(-5x + y = -2\)

\(-3x + 6y = -12\)