I'd like to have some math induction showing as below.(In an align environment \begin{align*}...\end{align*}) How can I have the "by addition" text at the end of the line? I tried with \cline but failed to do that.
x = 1 y = 2
-------------- by addtion
x + y = 3 z = 3
--------------------------------- by addition
x + y + z = 6
Here is what I've got so far. I also wanted the equations to be centered but I found it was hard to do.
\begin{align*}
x = 1 & y = 2 \\
\cline{1-2}
x + y = 3 & & z = 3 \\
\cline{1-3}
&x + y + z = 6& \\
\end{align*}


