Living by every word that comes from the mouth of God
means trusting in his provision, and indeed, God did provide angels to provide for Jesus (Matthew 4:11) after Jesus passed the test.
The emphasis in this passage falls upon the fact that it is God who provides and gives. Faith means trusting in God to provide. Jesus is standing at the start of his ministry in the wilderness, and as such he knows that he will not starve to death, for God will provide whatever is necessary for sustaining him. Jesus therefore here applies the general principles of faith in God to his particular situation.1
Jesus here teaches us that all people are dependent upon the words from God’s mouth. When you listen to God, you will be satisfied, regardless of the means by which this satisfaction is brought about. The heart of Jesus’ answer is that he awaits what God will say with regard to satisfying his hunger and that he desires to maintain that attitude of dependence throughout the temptation. His faith was tested through the hunger, but it passed the test and was not ashamed when the angels came to serve him (Matthew 4:11).2
4 But he answered, “It is written, “‘Man shall not live by bread alone, but by every word that comes from the mouth of God.’”