Updated answer after question was edited to state that the flowers are bluish purple: This is not garlic mustard, which has white flowers. It does not look like any violets I've seen, and not exactly like the creeping charlie we have here either. Sorry I am not able to help after all.
Previous answwer: This looks an awful lot like garlic-mustard, which we also have here in the Fingerlakes region of NY. It is a noxious weed and hard to eradicate. I have had some luck pulling it up, but it's a constant battle. The real key is keeping it from going to seed, which happens during the 2nd year. If you can hand pull the 1st year plants (make sure you get all of the root), they won't go to seed, but it sounds like you probably have a bunch of seeds already in your soil, so you'll be pulling plants from the old seeds for a while :(
Here's a link to a WA state website I found with photos & info that may be helpful to you. http://www.kingcounty.gov/environment/animalsAndPlants/noxious-weeds/weed-identification/garlic-mustard.aspx
If you look at the photos there and think this is what you have, you can search for other methods of control if hand pulling is not practical.