Asked by kymari davis-shanks
page 19 of 19
One Solution, No Solution, or Many Solutions Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. The dashed line passes through left parenthesis negative 7 comma 0 right parenthesis and left parenthesis 7 comma 0 right parenthesis.
Does the graph show the system of equations x+y=2
and −x+y=7
? Should the lines for the system be parallel?
(1 point)
Responses
The graph of x+y=2
is incorrect. The lines should intersect.
The graph of x plus y equals 2 is incorrect. The lines should intersect.
Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=7
is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.
The graph of −x+y=7
is incorrect. The lines should intersect.
One Solution, No Solution, or Many Solutions Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. The dashed line passes through left parenthesis negative 7 comma 0 right parenthesis and left parenthesis 7 comma 0 right parenthesis.
Does the graph show the system of equations x+y=2
and −x+y=7
? Should the lines for the system be parallel?
(1 point)
Responses
The graph of x+y=2
is incorrect. The lines should intersect.
The graph of x plus y equals 2 is incorrect. The lines should intersect.
Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=7
is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.
The graph of −x+y=7
is incorrect. The lines should intersect.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve this problem, let’s break down the given equations and their graphical representations.
1. **Equations**:
- The first equation is \(x + y = 2\).
- The second equation is \(-x + y = 7\).
2. **Slope and Intercept**:
- For the equation \(x + y = 2\):
- Rearranging gives \(y = -x + 2\), which has a slope of \(-1\).
- For the equation \(-x + y = 7\):
- Rearranging gives \(y = x + 7\), which has a slope of \(1\).
3. **Determining Line Characteristics**:
- The first line (from \(x + y = 2\)) has a slope of \(-1\).
- The second line (from \(-x + y = 7\)) has a slope of \(1\).
- Since the slopes are different (\(-1\) and \(1\)), these lines will **intersect** at some point, which means there is **one solution** for the system.
4. **Graph Interpretation**:
- According to the problem, the graph shows the lines as **parallel**.
- Parallel lines would imply they do not intersect, indicating there would be **no solution** to the system of equations.
5. **Conclusion**:
- Since the two lines are not parallel (due to different slopes), the graphs provided in the question must be incorrect.
- Therefore, the correct answer from the responses would be:
- **The graph of \(-x+y=7\) is incorrect. The lines should intersect.**
This response indicates that the representations shown in the graph do not correctly reflect the nature of the equations provided.
1. **Equations**:
- The first equation is \(x + y = 2\).
- The second equation is \(-x + y = 7\).
2. **Slope and Intercept**:
- For the equation \(x + y = 2\):
- Rearranging gives \(y = -x + 2\), which has a slope of \(-1\).
- For the equation \(-x + y = 7\):
- Rearranging gives \(y = x + 7\), which has a slope of \(1\).
3. **Determining Line Characteristics**:
- The first line (from \(x + y = 2\)) has a slope of \(-1\).
- The second line (from \(-x + y = 7\)) has a slope of \(1\).
- Since the slopes are different (\(-1\) and \(1\)), these lines will **intersect** at some point, which means there is **one solution** for the system.
4. **Graph Interpretation**:
- According to the problem, the graph shows the lines as **parallel**.
- Parallel lines would imply they do not intersect, indicating there would be **no solution** to the system of equations.
5. **Conclusion**:
- Since the two lines are not parallel (due to different slopes), the graphs provided in the question must be incorrect.
- Therefore, the correct answer from the responses would be:
- **The graph of \(-x+y=7\) is incorrect. The lines should intersect.**
This response indicates that the representations shown in the graph do not correctly reflect the nature of the equations provided.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.