Question
Ms. Mac asked her students to determine a solution for 2x−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.
.
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.
Answers
GPT-4o mini
To determine which points are solutions to the equation \(2x - 5y = 9\), we will substitute the given points into the equation.
1. **Testing Bella's point (-2, 1)**:
\[
2(-2) - 5(1) = -4 - 5 = -9 \quad \text{(not equal to 9)}
\]
So, (-2, 1) is **not a solution**.
2. **Testing Marco's point (11, 2)**:
\[
2(11) - 5(2) = 22 - 10 = 12 \quad \text{(not equal to 9)}
\]
So, (11, 2) is **not a solution**.
3. **Testing Liam's point (2, -1)**:
\[
2(2) - 5(-1) = 4 + 5 = 9 \quad \text{(equal to 9)}
\]
So, (2, -1) is a **solution**.
Now, we can determine the positions of these points relative to the graph of the equation \(2x - 5y = 9\).
- **Point that is a solution**:
- (2, -1)
- **Point that is not a solution and lies above the graph**:
- Since the point (11, 2) has a higher value when substituting in (producing 12 instead of 9), it lies above the graph.
- **Point that is not a solution and lies below the graph**:
- Since (-2, 1) produces -9 when substituted (much less than 9), it lies below the graph.
In summary:
- Point that is a solution: **(2, -1)**
- Point that is not a solution and lies above the graph: **(11, 2)**
- Point that is not a solution and lies below the graph: **(-2, 1)**
1. **Testing Bella's point (-2, 1)**:
\[
2(-2) - 5(1) = -4 - 5 = -9 \quad \text{(not equal to 9)}
\]
So, (-2, 1) is **not a solution**.
2. **Testing Marco's point (11, 2)**:
\[
2(11) - 5(2) = 22 - 10 = 12 \quad \text{(not equal to 9)}
\]
So, (11, 2) is **not a solution**.
3. **Testing Liam's point (2, -1)**:
\[
2(2) - 5(-1) = 4 + 5 = 9 \quad \text{(equal to 9)}
\]
So, (2, -1) is a **solution**.
Now, we can determine the positions of these points relative to the graph of the equation \(2x - 5y = 9\).
- **Point that is a solution**:
- (2, -1)
- **Point that is not a solution and lies above the graph**:
- Since the point (11, 2) has a higher value when substituting in (producing 12 instead of 9), it lies above the graph.
- **Point that is not a solution and lies below the graph**:
- Since (-2, 1) produces -9 when substituted (much less than 9), it lies below the graph.
In summary:
- Point that is a solution: **(2, -1)**
- Point that is not a solution and lies above the graph: **(11, 2)**
- Point that is not a solution and lies below the graph: **(-2, 1)**