Sylvie finds the solution to the system of equations by graphing. y = x + 1 and y = x – 1 which graph shows the solution to sylvie’s system of equations? image for option 1 image for option 2 image for option 3 image for option 4

The only solution is when y=y

x+1=x-1  subtract x from both sides

1=-1

This is never true so there are no solutions.  In this case it is due to the fact that both lines have the same slope and different y-intercepts.  This means that they are parallel lines that have a constant distance between them.