To develop a third equation, we will consider the deflection of the beam at point C. The steps involved in this process can be outlined as follows.

• We will replace the post with an unknown force C_y.
• Using the method of superposition, we will derive an expression for the beam deflection at C in terms of C_y.
• We'll take into account the deformation of the post (1) due to the force it carries.

These steps will produce a equation in terms of C_y based on the deflection of the beam at C. This type of equation is known as a compatibility equation.