I'll give it a try. Suppose you have two equations known to be true, say x=y and u=v. For either equation, I should be able to add the same thing to both sides of the equal sign and still have a true equation, i.e., x+u=y+u. Agreed? But since u=v, we could also write this as x+u=y+v, and that must also be true. The last statement is equivalent to adding the 2 equations, but we could have also subtracted, or taken any linear combination.