Suppose two 2D Bézier curves of the same degree but different control points. $\gamma_1(t) = \Sigma_{i=0}^n B_{i,n}(t) q_i$ and $\gamma_2(t) = \Sigma_{i=0}^n B_{i,n}(t) Q_i$
where $q_0 = Q_0 = (0;0), q_n = Q_n = (1;0)$ and $q_i \neq Q_i$
Let $y_1(x)$ and $y_2(x)$ be their Cartesian forms.
Suppose a third curve which is the sum of the two previous curves w.r.t Y axis i.e. $y_3(x) = y_1(x) + y_2(x)$.
Is it possible to express $y_3(x)$ as a parametric curve $\gamma_3(t)$ using either Bézier curves, B-splines or even NURBS ?