[BG3] If I multiclass Wizard/Sorcerer, which ability score is used for spell save DCs, spell attacks, etc?

Given what I've read about BG3 allowing anyone with at least one level of Wizard learning any spell for which they have slots, and how 5e in general handles spell slots for multiclass casters, I'm thinking to make a Wizard 1/Sorcerer X character, and using the ability to learn from scrolls to remove the limited spell pool weakness from the sorcerer. But then I was thinking - are they Wizard spells if I learn them that way? And if so, will they use INT for attack rolls and save DCs?

I don't have a save file with a high level character that I can just respec to try it out, so I'd appreciate if someone could try it out or just share if they already know the answer. Thanks!

EDIT: Looks like BG3 maintains separate spellbooks, which makes it clear which spells are which and therefore which ability is used. I confirmed that as a Wizard 1/Sorcerer 3 I could learn a level 2 spell from a scroll, which confirms that a Wizard 1/Sorcerer 11 could focus on learning offensive spells with Sorcerer levels, and utility/defensive spells from scrolls.