What are these plants and are they invasive?
The first one with the yellow flowers is called fig buttercup a.k.a. lesser celandine. It is extremely invasive and spreads widely and displaces native plants.
It is a spring ephemeral, meaning that it disappears by early June. If your patch is small, you should pull or dig it up, removing as many of the tubers as possible. If it's large, you can use a non-selective herbicide with the active ingredient glyphosate.
The second looks like our native violets. They are lovely (and edible), but many people do not like them in their lawns, as they do spread. Otthers, keep them.