Why did the LORD save Jerusalem: because Hezekiah prayed, or for David's sake?

The chapter gives both, in the LORD's own words. To Hezekiah: "You have prayed to me against Sennacherib king of Assyria, and I have heard you" (19:20). Of the city: "For I will defend this city to save it, for my own sake and for my servant David’s sake" (19:34). And to the king of Assyria he names what the king had done against him: "Because of your raging against me, and because your arrogance has come up into my ears" (19:28). "For David's sake" is not new in Kings. Solomon was told that one tribe would be given to his son "for David my servant’s sake, and for Jerusalem’s sake which I have chosen" (1 Kings 11:13), and in Jehoram's days "the LORD would not destroy Judah, for David his servant’s sake" (8:19). In the next chapter the LORD says it again, when Hezekiah is sick: "I will defend this city for my own sake, and for my servant David’s sake" (20:6). The chapter doesn't set these reasons against each other. It gives them side by side.