This is just a picture of the lawn from afar. The close up weed in the picture before is all the green spots in the lawn.

Lawn weed killers kill broadleaf stuff but not grass.

The green plants in your lawn are grass, a weedy grass that's a different kind than the Bermuda.

Looks to me it would be easy to pull each green clump, roots & all. Do it before the stuff blooms & sets seed.

As Jean said that is a grass and none of the broad leaf "weed" poisons will do anything to it. For proper ID you could take a plant to your counties office of your University of Arizona Cooperative Extension Service.
To begin working on getting rid of it you need to know about your soil, the soils pH and nutrient levels and the amouint of organic matter in that soil because many of these plants can indicate soil conditions and will grow better in soils that the grasses we want will not. So while at the CES office ask about soil testing and also dig in with these simple soil tests,
1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drainsâ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.
to learn more about that soil.

Here is a link that might be useful: UA CES