With any equation, the value of the things on the left, and the value of the things on the right of the equals sign are the same. You may not know what they are, but you do know that they have the same value.
You also know that you can add an equal amount to both sides of any equation, while maintaining equality.
So if X = 5, then X + 1 = 5 + 1.
Adding an equation to an existing equation is the same as adding the 1s above, except that you don't know the value of what you added yet. You just know that you added the same amount to both sides, because your equal sign tells you the values are the same.
What might make this completely obvious would be to solve everything out like you normally do. Then after you're done, go back and plug your values into the equation that you added to the other equation. What you'll find is that both sides evaluate to the same value. Thus when you added each of those sides to the other equation, you were simply adding some unknown amount (known now that you solved it.)
I hope that helps. It might be easier to work through with an example.
