Yard looks like fescue so you have it easy.
- - pull as many weeds, crabgrass, etc by hand as possible to remove seeds
- - spray with weed killer when you have lots of small ones too cumbersome to pull (have multiple choices and even spray that will just kill Bermuda that is in your fescue)
Areas with wholesale weeds (ie hopeless) . . NUKE the whole area with Round-Up and start over with re-seeding, after you roto-til and improve the soil.
= = = = = =
Now compare to Zoysia yard I'm trying to keep "pure" Zoysia (very slow growing warm season grass). I've found at least 2 varieties of Bermuda that I either dig very deep to remove roots, or kill with RoundUp and also kill some of my Zoysia (not good as hard to grow). All neighbors around have bastardized variety of grabgrass, bermuda and fescue (ie whatever will grow). They don't water much if any, and I've got sprinkler system and water often. All those unwanted seeds end up growing in
my yard.
Only prevention for all those blowing seeds from neighbors is very healthy thick lawn that doesn't leave any "open dirt" for those ******* seeds to grow !!
Good luck . . . you'll NEVER win the War with Weeds !!
