Simple question about nodal analysis
Label the node where R8 connect to the vs source as Vd.

Now \$V_d = V_a - v_s\$.

So you can calculate \$I_8=\frac{V_d}{R_8}=\frac{V_a-v_s}{R_8}\$.

If you rearrange terms in your first equation, you'll find this is exactly what is accounted for in the node equation.

In your version you seem to have assumed \$I_8 = \frac{v_s-0}{R_8}\$. This doesn't make any sense because \$v_s\$ isn't applied across R8.