Summary of approach

Weak acids and weak bases react with water to less than 5%.
The initial  concentration and the equilibrium concentration of the member of the pair that is dissolved can be considered to be approximately equal.
 
If solute is[A] equals[HA] equals
only the acid
of the pair
[H3O+]*initial c(acid)
only the base
of the pair
initial c(base)Kw/[H3O+]**
both the acid and the base
of the pair
initial c(base)initial c(acid)

When a single member of the conjugate pair is dissolved, the stoichiometry of its reaction with water (shown below) can be used to relate the equilibrium concentration of its conjugate to pH.

*Each acid reacts to give one H3O+ and one base:
acid + H2O H3O+ + conjugate base
**Each base reacts to give one acid and one OH:
base + H2O conjugate acid + OH