What kind of grass (or weed) is this?

[Safroniabee]

We have a lawn company that comes and sprays for weeds, but this hasn't died after they came, so I'm not sure if it's a weed. We have had an incredibly difficult time getting grass to survive the summer in our back yard, as you can see in the second pic, but this patch is one of the only areas that has thrived. if it is a type of grass, I want to plant more of it!

[!potatoes!]

sure looks like some kind of grass.

[Mr_bobo_]

It can be Cynodon dactylon, very nasty one... same type as Agropiron repens... perennial grass...
Try to destroy it with selective-translocation herbicides for narrow-leaved weeds