If the testator makes provision by his will, or designates the estate to be appropriated for the payment of his debts, the expenses of administration, or the family expenses, they shall be paid according to the provisions of the will; but if the provision made by the will or the estate appropriated, is not sufficient for that purpose, such part of the estate of the testator, real or personal, as is not disposed of by will, if any shall be appropriated for that purpose.