Rearrange $x-y=1$ 
Given the equation $x-y = 1$, I want to rearrange it to solve for $y$. The answer in the learning materials I have is $y = x-1$.

When I try to rearrange the equation myself I go through the following thought process:
$x-y =1$
--- first I think I want to get the x over to the right hand side of the equals sign so that I'm left with the $-y$ on the left side. So I do minus $x$ on both sides:
$-y = 1-x$
---Then I'm thinking that I want to change the minus $y$ to positive $y$. So then I multiply both sides by minus $1$
$y = -1 + x$
--Then I assume I can just switch around the position of $-1$ and $x$ to give
$y = x-1$
My question is: Is this the same thought process that you would go through to solve this simple equation or am I taking too many unnecessary steps?
 A: The only way to do it more simply is this: It doesn't matter whether we solve for $y$ on the right or on the left. Thus, since $y$ is subtracted on the right, add it to both sides, and then subtract $1$ from each side to get $y$ alone over there: $$x-1=y.$$
There you have $y=x-1$, written the other way around.
I guess you could look at the original equation as telling you that taking $y$ away from $x$ leaves a remainder of $1$, which means that $y$ must be just $1$ less than $x$. Translate that sentence from words to symbols, and you have the same answer.
Is this what you were looking for?
A: Before:


*

*$x$ is on the left with a plus sign,

*$y$ is on the left with a minus sign,

*$1$ is on the right with a plus sign.
After:


*

*$x$ is on the $\color{red}{right}$ with a plus sign,

*$y$ is on the left with a $\color{red}{plus}$ sign,

*$1$ is on the right with a $\color{red}{minus}$ sign.
So chances are low that you can do in less than three elementary transformations... (Though you can reduce to two transformations if you allow the reversal $x-1=y$.)

My own way to think:
Isolate $y$ in two moves
$$x-y=1\to x=y+1\to x-1=y.$$
($y$ goes to the right to get a positive sign.)
