Alright, for the two equations you gave me, which are x=y+4 and y=x+4, we can try substitution to get the answer! Substitution is when you take one variable from one equation and plug it into another equation to find out what both variables are!
To do this, we start with the first equation, x=y+4. Then, from the second equation we know that y=x+4 so we can plug x+4 in for the y in the first equation. We now have x=(x+4)+4 as our first equation.
Now, we can simplify! The parenthesis aren't important in this equation, so we can just get rid of them, giving us x=x+4+4. Now we can simplify to give us x=x+8. Now, all that's left is to subtract the x from both sides of the equation! This gives us 0=8, but we know that that's not possible because there is no way that 0 can equal 8. This means that this equation doesn't have an answer!
To check this, you can repeat the steps above with the second equation, but you will still end up with 0=8, and that, again, means that this equation doesn't have an answer.