You can. It's a myth that you can't do both at the same time, particularly those who are new to weight/resistance training and especially if you are in the obese BMI.
You can also increase strength without building mass but the only way to know for certain if you are building lean mass while losing fat is to have your body fat tested monthly. If lean mass is increasing, while body fat is decreasing, you'd be building lean mass. However, it requires full body and heavy training to really build lean mass while losing fat. A few push ups may be increasing your strength and conditioning but you'd need to work your way up to a challenging full body routine to really let your body know that you need your fat/calories to be put toward building muscle. You also don't want your body to think it's starving or it won't be using those cals to build muscle, that would be low on its list of priorities. Adequate calorie intake, adequate protein and make every calorie count (ie; eat clean, nutrient dense foods, cut out all the junk).
You may find these links helpful:
scoobysworkshop.com/gain-muscle-lose-fat/<
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www.livestrong.com/article/327732-differen
ce-between-strength-training-muscle-bu
ilding/
Edited by: JENNILACEY at: 11/28/2013 (10:09)