These are colligative properties. More solutes means more things to get in the way of creating lattice structures when freezing, so more energy is required. This explains freezing point depression. Boiling point elevation is explained by the greater amount of intermolecular forces in a solution which means more energy is required to break them to enter the gaseous phase. This difficulty to leave the liquid is also what explains vapor pressure depression.
You can see here that they are just inverses of each other. But here's a case where they aren't.
Among branched alkanes, increased branching raises the melting point (=freezing point), and lowers the boiling point. Yet compared to unbranched alkanes, increased branching lowers both.