Multiplying a whole equation by a number that is not zero changes nothing that matters. 3x + 4y = 18 and 6x + 8y = 36 are true for exactly the same pairs (x, y), because you can divide back by 2 and return. Same line, new clothes.
Adding two true equations is just adding equals to equals: if A = B and C = D, then A + C = B + D. Anything that satisfied both equations still satisfies the sum.
The multiplier may never be 0. Multiplying by 0 turns an equation into 0 = 0 — true for every point in the plane. You would not have simplified the system, you would have thrown one equation away.