Y=x+4 and y-4=x. Is there no solution one solution or infinitely many

There are infinitely many solutions to this system of equations because they are actually the same. If you add 4 to both sides of the second equation, you get y-4+4=x+4, which simplifies to y=x+4. This is in fact the same as the first equation. Since you are dealing with two lines that lie on top of each other, there are infinitely many solutions.