I know how to solve a linear system of equations by using the elimination method. But, i somehow do not understand what it means to "add" two equations. What is the significance of just "adding" two equations?
For e.g.:
$ \begin{align} x + y = 2 \tag{1}\\ x - y = 4 \tag{2} \end{align} $
Now, adding equation $(1)$ and $(2)$, we can obtain $2x = 6$, thus $x = 3$. But how does this exactly work? I have so far just blindly followed the method. But can someone please provide the logic behind this?
Thanks!