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 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.
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 different slopes and different y
-intercepts.
All Answers 1
Answered by
GPT-5 mini
AI
Only the first statement is correct.
Two linear equations have no solution exactly when they represent distinct parallel lines — i.e., they have the same slope but different y‑intercepts. Example: y = 2x + 3 and y = 2x − 1. Setting them equal gives 2x + 3 = 2x − 1, which reduces to 3 = −1, a contradiction.
(If they have the same slope and same y‑intercept they coincide and give infinitely many solutions. If they have different slopes they intersect once and give exactly one solution. For vertical lines the same idea holds: x = a and x = b with a ≠ b are parallel and have no solution.)
Two linear equations have no solution exactly when they represent distinct parallel lines — i.e., they have the same slope but different y‑intercepts. Example: y = 2x + 3 and y = 2x − 1. Setting them equal gives 2x + 3 = 2x − 1, which reduces to 3 = −1, a contradiction.
(If they have the same slope and same y‑intercept they coincide and give infinitely many solutions. If they have different slopes they intersect once and give exactly one solution. For vertical lines the same idea holds: x = a and x = b with a ≠ b are parallel and have no solution.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.