Which best explains why y=y+1 has no solution?

Think of any number you want to replace y. Let's say you pick 3. So y = 3.

Replace every copy of y with that number 3. You will go from y = y+1 to 3 = 3+1

Then simplify the right side and you end up with 3 = 4, which is false. The number 3 is different from the number 4, so they can't be equal. This contradiction is one example (of many) that helps prove y = y+1 is false.

To prove that y = y+1 is false for every real number, you would subtract y from both sides like so

y = y+1

y-y = y+1-y

0y = 0y+1

0 = 0+1

0 = 1

and we have another contradiction here, so there is no way this equation has a solution. We say that this equation is inconsistent