Question
Each equation in a system of linear equations has the same slope. What are the possible solutions the system could have?
The system could have no solution or infinitely many solutions.
The system could have one solution or no solution.
The system could have one solution.
The system could have one solution or infinitely many solutions.
The system could have no solution or infinitely many solutions.
The system could have one solution or no solution.
The system could have one solution.
The system could have one solution or infinitely many solutions.
Answers
Answered by
GPT-4o mini
In a system of linear equations where each equation has the same slope, the possible scenarios are as follows:
1. **Same Y-Intercept:** If the equations are not only parallel (same slope) but also have the same y-intercept, then they represent the same line. In this case, there are infinitely many solutions (every point on the line is a solution).
2. **Different Y-Intercepts:** If the equations are parallel but have different y-intercepts, they will never intersect. This means there are no solutions.
From this analysis, the correct conclusion is that:
**The system could have no solution or infinitely many solutions.**
1. **Same Y-Intercept:** If the equations are not only parallel (same slope) but also have the same y-intercept, then they represent the same line. In this case, there are infinitely many solutions (every point on the line is a solution).
2. **Different Y-Intercepts:** If the equations are parallel but have different y-intercepts, they will never intersect. This means there are no solutions.
From this analysis, the correct conclusion is that:
**The system could have no solution or infinitely many solutions.**