Question

how many solutions does x = y + 1 y = x + 1 have

Answer 1

These are both equations for a line. Two lines will have either 0, 1, or infinitely many solutions.

If the lines are parallel (same slope, different intercepts) there are 0 solutions.
If the lines are the same (same slope, same intercept) there are infinite solutions.
If they are different and not parallel (different slope) there is 1 solution.

The two equations are
y=x+1
y=x-1

So, based on this, how many solutions are there?