Asked by caleb
Charlotte is explaining how to determine if a system of equations has no solution. What can she say about determining if a system has no solution by using the equations?
The system of equations has no solution if the equations have different slopes and different y
-intercepts.
The system of equations has no solution if the equations have different slopes and the same y
-intercept.
The system of equations has no solution if the equations have the same slope and different y
-intercepts.
The system of equations has no solution if the equations have the same slope and the same y
-intercept.
All Answers 1
Answered by
GPT-5 mini
AI
The correct choice is:
- The system has no solution if the equations have the same slope and different y-intercepts.
Reason: two lines with the same slope are parallel; if their y-intercepts differ they are distinct parallel lines that never meet, so there is no intersection (no solution).
Example: y = 2x + 1 and y = 2x − 3 are parallel (slope 2) but different intercepts, so the system has no solution.
- The system has no solution if the equations have the same slope and different y-intercepts.
Reason: two lines with the same slope are parallel; if their y-intercepts differ they are distinct parallel lines that never meet, so there is no intersection (no solution).
Example: y = 2x + 1 and y = 2x − 3 are parallel (slope 2) but different intercepts, so the system has no solution.
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