rear bike rack compatibility I am looking to install a rear bike rack on by 26" MTB. I don't want to spend so much so I'm looking to just grab something from a thrift store from bikes like these .

Will installing these to my MTB work?
If you mean literally the pictured racks, then generally speaking no, or at least not well, unless by chance. The racks in the picture both have non-adjustable upper stays; they're made in specific dimensions to fit and be level on a specific bike, whereas bikes as a whole have rack attachment points spanning all sorts of different dimensions. Racks that come with bikes, especially older ones, are often like this. To get something that you know or at least strongly suspect will work, you should get a normal aftermarket rack with adjustable stays, which you can probably still find used if you look.