This is a point of much contention between professional trainers, weight lifters, and body builders. There seems to be no agreed upon answer to the question of which muscle groups to workout together. You can either lift opposite muscle groups, such as biceps and triceps together, back and chest together. Or you can lift complementary muscle groups together, such as back and biceps in one workout, chest and triceps in another. In my opinion, it’s mostly a matter of preference, although there are some definite benefits to each.

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Working Out Opposite Muscle Groups
When you pair opposite muscle groups together, you are choosing to work muscles that will have very little effect on each other in your workout. Normally, this is a combination of push/pull exercises. For example, almost all back exercises involve the pulling motion (barbell row, lat pull-down, seated row, etc.), whereas nearly every chest movement is a pushing exercise (bench press, inclined bench press, dips). This benefits you because you do not work your back at all while working your chest, so your back muscles are not fatigued before you even get to that portion of the workout. However, one drawback to pairing opposite muscle groups is that the following workout day you will likely have to work a complementary muscle. If you do triceps in Workout A, then you will have to do chest in Workout B. Your triceps may be fatigued from the previous day’s workout, which can have adverse effects on your chest routine. Another disadvantage when compared with complementary workouts is that you will not have the benefit of warming up your triceps during your chest routine, or your biceps during your back routine, so you will have to stretch or warm them up on their own to help prevent injury.
Working Complementary Muscle Groups
Complementary muscles, such as chest and triceps, are often paired together in a workout. This is because they are involved in many of the same movements. When you do bench press, your main focus is usually on your chest, but you are also giving your triceps a bit of a workout as well. This helps to warm up the complementary muscle, but it can also hurt by fatiguing your muscle before you get to it. If you always do chest before triceps, then you will never be able to do as much weight on your skull crushers or your cable press-downs because your tris will already be a little tired. And you definitely cannot train triceps first, because if you do you won’t be able to lift as heavy on the bench. However, the advantage here is that in your next workout (assuming it is back and biceps, in this case) neither muscle group will have been worked at all the day previously, ensuring optimal rest and growth.
I’ve switched back and forth a few times myself. I was training opposite muscles together for about a year, for the benefits listed in the first paragraph above. However, currently (and for the past 3 months) I have been training complementary groups together, and I like this method and the results I am seeing as well. Until there is any scientific evidence that one way is superior to the other, just go with what works best for you. Train opposite pairs together for a couple weeks, then try muscles that complement each other, and figure out what you like best.