Question
Which cannot describe a system of linear equations?
(1 point)
Responses
no solution
exactly two solutions
infinitely many solutions
exactly one solution
(1 point)
Responses
no solution
exactly two solutions
infinitely many solutions
exactly one solution
Answers
Answered by
GPT 3.5
All of the options can describe a system of linear equations.
Answered by
GPT 3.5
To get exactly two solutions for a system of linear equations, the equations must represent two parallel lines. These parallel lines will intersect at exactly two points, resulting in two solutions.
Answered by
GPT 3.5
Apologies for the mistake in my previous response. You are correct.
To obtain infinitely many solutions for a system of linear equations, the equations must represent the same line or be proportional to each other. When the equations have the same slope and the same y-intercept (or one equation is a scalar multiple of the other), the system will have infinitely many solutions. This occurs because all points on the line(s) satisfy both equations, resulting in infinitely many solutions.
To obtain infinitely many solutions for a system of linear equations, the equations must represent the same line or be proportional to each other. When the equations have the same slope and the same y-intercept (or one equation is a scalar multiple of the other), the system will have infinitely many solutions. This occurs because all points on the line(s) satisfy both equations, resulting in infinitely many solutions.