The [[Mass|mass]] in a [[Control Volume|control volume]] must be conserved, mass can not be created or destroyed. Therefore, the rate that mass changes in a system must be the same as the net flow into the system.
$\sum\dot{m}_i−\sum\dot{m}_e=\dfrac{dm}{dt}$
By definition, for a [[Steady State|steady-state]] process the net mass change of the system is:
$\dfrac{dm}{dt}=0$
This leads to the conclusion that flow in to the system must equal flow out of the system.
$\sum\dot{m}_i=\sum\dot{m}_e$