A solution that contains a system at equilibrium is the one in which there is no change in color
If the color of the solution changes slowly it means that the equilibrium shifts towards the right. This happens when we add the reactant and the equilibria move towards the right that is away form the reactant increasing the product formation. But when there is no change in color it means the reaction is constant and there is a state where the concentrations of reactant and product are not changing and are constant.
Hence, the solution in which the color is not changing is at equilibrium.
A reactionis said to be at equilibrium when the rate of forward reaction equals the rate of reverse reaction. That means the rate at which the product is formed equals the rate at which the reactants are reformed. The colour of the solution does not change at this point because the both reactions are exactly balanced.