x+y = 5 (1)
x-y = 4. (2)
If you wanted to get rid of the xs, then you subtract 1 from 2, OR subtract 2 from 1 since both xs are positive in both equations. When you have two positive numbers, and you want to get 0, then you have to subtract one from the other.
To get rid of the ys you have to ADD (1) to (2), OR subtract (2) from (1), because one is positive and one is negative. When you have 1 negative number, one positive number, you have to subtract the negative from the positive, or add the negative to the positive.
In another example:
x-y = 5 (1)
-x-y = 4 (2)
Here, if you want to get rid of the xs, you use the rules from above! But if you want to get rid of ys, then you have to subtract (1) from (2), OR (2) from (1), since they are both negative.
And indeed, if you had two equations in which x and y have different coefficients, then you multiply both or one of the equations by whatever is necessary to get a common coefficient.