Which statement best describes the system of equations {y=−3x+7y=−3x−7
?(1 point)
Responses
The equations have different slopes, but they share the same y-intercept, (0,−3). Thus, the system has one solution at (0,−3).
The equations have different slopes, but they share the same y -intercept, left parenthesis 0 comma negative 3 right parenthesis . Thus, the system has one solution at left parenthesis 0 comma negative 3 right parenthesis .
Both equations have a slope of −3, and they share the same y-intercept. Thus, the system has an infinite number of solutions because they are identical lines.
Both equations have a slope of negative 3 , and they share the same y -intercept. Thus, the system has an infinite number of solutions because they are identical lines.
Both equations have a slope of −3, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel.
Both equations have a slope of negative 3 , but they do not share the same y -intercept. Thus, the system has no solutions because the lines are parallel.
The equations have different slopes and different y-intercepts. Thus, the system has one solution at (−3,7).
The equations have different slopes and different y -intercepts. Thus, the system has one solution at left parenthesis negative 3 comma 7 right parenthesis .
?(1 point)
Responses
The equations have different slopes, but they share the same y-intercept, (0,−3). Thus, the system has one solution at (0,−3).
The equations have different slopes, but they share the same y -intercept, left parenthesis 0 comma negative 3 right parenthesis . Thus, the system has one solution at left parenthesis 0 comma negative 3 right parenthesis .
Both equations have a slope of −3, and they share the same y-intercept. Thus, the system has an infinite number of solutions because they are identical lines.
Both equations have a slope of negative 3 , and they share the same y -intercept. Thus, the system has an infinite number of solutions because they are identical lines.
Both equations have a slope of −3, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel.
Both equations have a slope of negative 3 , but they do not share the same y -intercept. Thus, the system has no solutions because the lines are parallel.
The equations have different slopes and different y-intercepts. Thus, the system has one solution at (−3,7).
The equations have different slopes and different y -intercepts. Thus, the system has one solution at left parenthesis negative 3 comma 7 right parenthesis .
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the given system of equations:
1. **Equations Given**:
- \(y = -3x + 7\)
- \(y = -3x - 7\)
2. **Slopes**:
- Both equations have a slope of \(-3\).
3. **Y-Intercepts**:
- The first equation has a y-intercept at \( (0, 7) \).
- The second equation has a y-intercept at \( (0, -7) \).
4. **Parallel Lines**:
- Since both lines have the same slope but different y-intercepts, the lines are parallel.
5. **Conclusion**:
- Lines that are parallel do not intersect at any point, meaning the system has no solutions.
Thus, the best statement that describes the system of equations is:
"Both equations have a slope of -3, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel."
1. **Equations Given**:
- \(y = -3x + 7\)
- \(y = -3x - 7\)
2. **Slopes**:
- Both equations have a slope of \(-3\).
3. **Y-Intercepts**:
- The first equation has a y-intercept at \( (0, 7) \).
- The second equation has a y-intercept at \( (0, -7) \).
4. **Parallel Lines**:
- Since both lines have the same slope but different y-intercepts, the lines are parallel.
5. **Conclusion**:
- Lines that are parallel do not intersect at any point, meaning the system has no solutions.
Thus, the best statement that describes the system of equations is:
"Both equations have a slope of -3, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel."
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