What I know is that when we make changes a system at equilibrium we use Le Chatelier rule, but it doesn't apply on this case..
The rule applies to non-equilibrium and explains what a perturbed system will do to achieve an equilibrium state again.
Le Chatelier's principle says:
"If a chemical system at equilibrium experiences a change in concentration, temperature, volume, or partial pressure, then the equilibrium shifts to counteract the imposed change and a new equilibrium is established."
that's unless I misunderstood the rule or your post.
an example on what I was asking for: if the fraction between products and reactants is more than K and we change temperature or the vessel volume for example, what will happen?
You give exactly the Wikipedia version. Once again Wikipedia must be taken with suspicion [1].
First, the Le Chatelier's principle is not a principle but a theorem: the
Le Chatelier & Braun theorem of moderation. This theorem can be derived from the thermodynamic stability theory based in the production of entropy (sometimes named the Prigogine-Defay method).
Second, if the system is at equilibrium, Le Chatelier & Braun says nothing. It is only when the system is perturbed and
shifts away from equilibrium that Le Chatelier & Braun says you what the system will do to achieve again an equilibrium. Example consider the equilibrium
A + B
C
Le Chatelier & Braun says nothing. Now add some amount of A. The system is not at equilibrium and Le Chatelier & Braun says that
A + B
C
up to that a new equilibrium state is reached.
Third, contrary to Wikipedia, Le Chatelier & Braun does not apply to changes in volume. From the section
C. The Le Chatelier-Braun theorem of moderation [2]:
But these theorems of restraint or of moderation cannot be applied in the same manner when we use other variables. If we decrease the volume of a system, the reaction produced does not tend to moderate this decrease.
Fourth, "if the fraction between products and reactants is more than K and we change temperature" what will happen depends. Is the concentration away from equilibrium because of some perturbation or because the system is in a stationary state maintained by flows? If it is the first case, Le Chatelier & Braun applies to the non-equilibrium state as always, it does not matter if non-equilibrium was achieved due to variation in concentration, temperature or both at once.
The general procedure to know what a chemical reaction will do against perturbation is to apply non-equilibrium thermodynamic theory.
[1] The academic level of many Wikipedia articles is the reason which I started the reference work presented in the Educative forum.
[2] 2A Equilibrium, Stability, and Displacements, 1971: In Physical Chemistry, An Advanced Treatise Volume I/Thermodynamics; Academic Press, Inc.; Wilhelm Jost (Editor). Sanfeld, A.