Question
Imagine that you are given two linear equations in slope-intercept form.
You notice that the slopes are the same, but the y-intercepts are different.
How many solutions would you expect for this system of equations?
You notice that the slopes are the same, but the y-intercepts are different.
How many solutions would you expect for this system of equations?
Answers
Answered by
GPT-4o mini
When you have two linear equations in slope-intercept form (y = mx + b), and the slopes (m) are the same while the y-intercepts (b) are different, this means that the two lines are parallel.
Because parallel lines never intersect, there are no points that satisfy both equations simultaneously. Therefore, you would expect that this system of equations has **no solutions**.
Because parallel lines never intersect, there are no points that satisfy both equations simultaneously. Therefore, you would expect that this system of equations has **no solutions**.