ok.. i just noticed you havent had the car long
So I assume its always done this..
um.. first i suggest you pull out the bulbs n check they're actually plugged in OR if they're not blown.
The bulbs should always come on at some point when you start the car. They only go off if everythings ok.
As they're not coming on either the bulbs are gone or not connected.
I know when the airbag tripped on my old car i just unplugged the connector from the bulb (however i told the people that bought the car the airbags were disabled)
_both_ being out stinks of them both being disconnected to hide an underlying ABS fault.. hopefully the airbag one was just disconnected to divert attention away from this other light staying on when you bought the car.
Oh and a final thing... For both ABS and airbag problems gettnig the car on a fault code reader will show exactly what/where the problem is. Some specialists will do this for free... some charge a little.
Pop the bulb holders off the dash and check what happens order then holla back!
Right now my moneys on them both coming on, and the airbag light going out.