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?
$\endgroup$ 12 Answers
$\begingroup$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?
$\endgroup$ 6 $\begingroup$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.)
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