I'm studying basic polynomial math online and I ran into this situation:
$$\begin{cases}2a + b = 8 \\ a + b = 5\end{cases}$$
The course material infers, using this exact notation, that:
$$2a + b = 8 - (a + b = 5) = a = 3$$
I was staring at this for a while and couldn't put it together, and then I realized that: $$\begin{cases}(2a-a) + (b-b) = 8-5\\ a = 3\end{cases}$$
This all seems logical but what I wonder is: Why can you do this? I've been rooting around the net but I can't seem to find the relevant name for this. I think it's called elimination but I don't know what branch of mathematics it falls under.
It's about substitution, that it always is allowed to replace equal expressions with each other. That's the essential property of equality.
Since $2a+b=8$ and $a+b=5$, the substitutions are allowed:
$a=(2a+b)-(a+b)=8-5$