If a player draws a card with Sylvan Library and chooses to keep it, do they pay 4 life per extra card kept?

Sylvan Library reads: 'At the beginning of your draw step, you may draw two additional cards. If you do, choose two cards in your hand drawn this turn. For each of those cards, pay 4 life or put the card on top of your library.' The key point is that the 4-life payment applies to each extra card you drew that you want to keep in your hand.

Under CR 400.7 and the card's own triggered ability, after you draw the two bonus cards, you must select two cards drawn this turn and then make a choice for each: pay 4 life or return it to the top of your library. You can mix and match — pay for one and return the other — or pay 8 life total to keep both, or return both for free.

If you only drew your normal one card for the turn (and did not activate the extra draw), Sylvan Library does nothing beyond its trigger resolving with no effect, since you have no extra cards to account for. The 4-life option only matters when you actually draw the additional cards.

Concrete example: It's your draw step. Sylvan Library triggers; you choose to draw two extra cards, so you draw three cards total this turn. You like all three but only your original draw is 'free.' You must pick two of the three drawn-this-turn cards and decide: pay 4 life each to keep them, or put them back. To keep both extras, you pay 8 life total.

Relevant rules: CR 120.1 (drawing cards), CR 603.3 (triggered abilities at start of step), and the Oracle text of Sylvan Library itself govern this interaction.