Question
Ms. Mac asked her students to determine a solution for 2x−5y=92x−5y=9. Bella believes (-2, 1) is a solution to the equation. Marco believes (11, 2) is a solution to the equation. Liam believes (2, -1)is a solution to the equation. (1 point) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Response area named a point that is a solution that lies on the graph of the equation. Response area named a point that is not a solution and lies above the graph of the equation. Response area named a point that is not a solution and lies below the graph of the equation. MarcoLiamBella
Answers
GPT-4o mini
Let's evaluate each of the points given:
1. **Bella's point**: (-2, 1)
- Substitute x = -2 and y = 1 into the equation 2x - 5y = 9:
\[
2(-2) - 5(1) = -4 - 5 = -9 \neq 9
\]
Therefore, Bella's point is not a solution.
2. **Marco's point**: (11, 2)
- Substitute x = 11 and y = 2 into the equation 2x - 5y = 9:
\[
2(11) - 5(2) = 22 - 10 = 12 \neq 9
\]
Therefore, Marco's point is not a solution.
3. **Liam's point**: (2, -1)
- Substitute x = 2 and y = -1 into the equation 2x - 5y = 9:
\[
2(2) - 5(-1) = 4 + 5 = 9
\]
Therefore, Liam's point is a solution.
Now, based on these evaluations, we can classify the points:
- **A point that is a solution that lies on the graph of the equation**: Liam (2, -1)
- **A point that is not a solution and lies above the graph of the equation**: Marco (11, 2); since it yields a value greater than 9.
- **A point that is not a solution and lies below the graph of the equation**: Bella (-2, 1); since it yields a value less than 9.
So, here is the classification for your response areas:
- A point that is a solution that lies on the graph of the equation: **Liam**
- A point that is not a solution and lies above the graph of the equation: **Marco**
- A point that is not a solution and lies below the graph of the equation: **Bella**
1. **Bella's point**: (-2, 1)
- Substitute x = -2 and y = 1 into the equation 2x - 5y = 9:
\[
2(-2) - 5(1) = -4 - 5 = -9 \neq 9
\]
Therefore, Bella's point is not a solution.
2. **Marco's point**: (11, 2)
- Substitute x = 11 and y = 2 into the equation 2x - 5y = 9:
\[
2(11) - 5(2) = 22 - 10 = 12 \neq 9
\]
Therefore, Marco's point is not a solution.
3. **Liam's point**: (2, -1)
- Substitute x = 2 and y = -1 into the equation 2x - 5y = 9:
\[
2(2) - 5(-1) = 4 + 5 = 9
\]
Therefore, Liam's point is a solution.
Now, based on these evaluations, we can classify the points:
- **A point that is a solution that lies on the graph of the equation**: Liam (2, -1)
- **A point that is not a solution and lies above the graph of the equation**: Marco (11, 2); since it yields a value greater than 9.
- **A point that is not a solution and lies below the graph of the equation**: Bella (-2, 1); since it yields a value less than 9.
So, here is the classification for your response areas:
- A point that is a solution that lies on the graph of the equation: **Liam**
- A point that is not a solution and lies above the graph of the equation: **Marco**
- A point that is not a solution and lies below the graph of the equation: **Bella**