Intuition behind Engel Aggregation and Cournot Aggregation
These expressions can be easily derived formally by taking the derivatives of Walras' law w.r.t $I$ (Engel aggregation) and $p_j$ (Cournot aggregation). 
The Engel aggregation means that not all goods are luxuries ($\eta_i&gt;1$), or necessities ($\eta_i&lt;1$), or inferior goods ($\eta_i&lt;0$). The Cournot aggregation says that the budget share $s_j$ of the good $j$  is small when the good $j$ has many substitutes ($\epsilon_{ij}&gt;0$), and big when it has many complements ($\epsilon_{ij}&lt;0$), or their respective budget shares are large.