When two equations have the same slope but different signs -/+ and he same y intercept is it infinite solution

Question

For example y=5/4+1 and y=-5/4+1

Answer 1

y = (5/4)x + 1 and y = (-5/4)x + 1

 

You get infinite solutions if two lines have the same slope and the same y intercept (y = (5/4)x+1 and y = (5/4)x+1).  You get no solutions if two lines have the same slope and different y-intercepts (y = 2x+1 and y = 2x -3).  In your problem you have the same y-intercept but two different slopes, 5/4 and -5/4, so there is only solution at (0,1).

Answer 2

Did you mean to leave out an x in the equations?

 

This answer assumes you meant y = 5x/4 + 1   and y = -5x/4 + 1

 

 

These two lines do intersect (cross). They have the same y-intercept (1) If their slopes were exactly the same but had different intercepts, they would be parallel and have no solutions. 

 

If the slopes were the same and the intercepts were the same, they would have infinite solutions because they are the same line.