Hosea 1:7

But I will have mercy. The spiritual condition of the southern kingdom, “the house of Judah,” was much better than that of the northern kingdom. Although there was a spiritual decline in Judah, the nation as a whole still held, in some measure, to the worship of God, to the Law, to the Temple services and to the sacrifices that pointed forward to the “Lamb of God, which taketh away the sin of the world” (John 1:29). This called forth divine compassion upon the southern kingdom in reproachful contrast with that denied the kingdom of Israel.

Will save them. God did save Judah from the fate suffered by Samaria in 723/722; he saved them later from Sennacherib by slaying the 185,000 in the Assyrian camp (2 Kings 19:35, 36; Isa. 37:36,37).

Will not save them by bow. Judah, though tainted with idolatry, did to a considerable degree maintain its devotion and trust in God rather than in military strength as did Israel. The detailed mention of armed forces here strikingly emphasizes the truth that when God delivers His people He does not need bow or sword, horses or horsemen, to gain the victory; and that these, when used, cannot save without Him (see Ps. 20:7; Isa. 31:1).