Will this benefit my weight loss?

I run on the elliptical for 1/2 hour daily and walk my dogs several times a week. I also do strength training 3x a week. I was thinking of adding a short yoga routine, about 20 minutes in the mornings.

1) will the yoga have any benefits at all? I'm not trying to lose a bunch solely through yoga, but will it help lean muscle or is it basically a waste of time

2) I'm trying to lose about 15 pounds and just generally tone and tighten. Will this routine help me achieve that in 4-5 months or is there something else I should be doing instead?
Will this benefit my weight loss?
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