Why Are We Saved Through Faith?

Jesus said to the woman, "Your faith has saved you; go in peace." (Luke 7:50 NIV)

"Receive your sight." Jesus told him. "Your faith has saved you." (Luke 18:42 CSB)

God has chosen faith to be the means of salvation because it glorifies Him.

The following quote is taken from "The Spurgeon Library | Saving Faith" where Charles Spurgeon gave the reason why faith was chosen as the instrument of salvation.

QUOTE
Faith is chosen by Christ to wear the crown of salvation because - let me contradict myself - it refuses to wear the crown. It was Christ that saved the penitent woman, it was Christ that saved that blind beggar, but he takes the crown from off his own head, so dear is faith to him, and he puts the diadem upon the head of faith and says, "Thy faith hath saved thee," because he is absolutely certain that faith will never take the glory to herself, but will again lay the crown at the pierced feet, and say, "Not unto myself be glory, for thou hast done it ; thou art the Saviour, and thou alone." In order, then, to illustrate and to protect the interests of sovereign grace, and to shut out all vain glorying, God has been pleased to make the way of salvation to be by faith, and by no other means.
UNQUOTE

For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast. (Ephesians 2:8-9 KJV)