Exercise machines vs. free weights

The short answer is yes, you can certainly do that. The only caveat here is that machines allow you to "concentrate" on a specific muscle or group of muscles. While this allows for sometimes "forced" good form in recruiting that solitary fiber, it's ignoring some of the very important stabilizing and supportive muscles that are important too! For example, if you're doing a leg press instead of a squat, you will recruit hamstring, quadriceps, some hip flexors and to a minimum extent, there will be abduction in the lower back/pelvis. A full squat will require the entire body to move (as it was intended to by nature) on the vertical plane, which causes all sorts of very important muscles, tendons, and bones to work in unison to achieve this task. As you may imagine, doing a concentrated muscle group may someday be more degenerative than beneficial, as some muscles overpower others, and you develop kinetic chain imbalances that can lead quite easily to injury.

However, if you're going to be quite modest about the whole thing, using poundage that does not possess the capacity to harm your joints and tendons, I would say, this is a completely viable way to train. Just be careful! Safety first.

what are your goals?

if you have any real world strength goals like being able to do a pushup, pullup, safely lift your kids, etc then free weights. if none of that matters then machines