Usually these cases involve infidelity - either she was cheating on him and it was a crime of passion (second-degree murder), or he found a new partner and needed to get rid of an inconvenient existing one (premeditated first-degree murder).
It looks like he killed her and died trying to dispose of her. But how do they whether he died trying to defend her and then she was killed and they we disposed together? Amazing they were found so quickly, with the car still running.