If two or more voltage sources $V_1$, $V_2$, ... $V_n$ are connected in series they can be replaced with a single voltage source with $$V_{eff}=\pm V_1 \pm V_2\pm...\pm V_n$$ where the terms in the right-hand side are taken with $+$ sign if the corresponding voltage source $V_i$ is oriented in the same direction with $V_{eff}$ and with $-$ sign if $V_i$ is oriented in opposite direction with $V_{eff}$. Since the voltage sources are all connected in series, when we replace $V_i$ with $V_{eff}$, the other voltage sources are replaced with short-circuits (i.e. wires).

For instance, consider the circuit in Fig. 1, in which voltage sources $V_1$ and $V_2$ are connected in series (because they belong to both the outer loop and loop $i_1$). In this circuit, we can keep one voltage source, say $V_1$, replace its value with $$\begin{equation}V_{1,eff}=V_1-V_2\end{equation}$$ and replace voltage source $V_2$ with a wire. Notice that $V_1$ appears with a positive sign in the equation above because $V_1$ and $V_{1,eff}$ have the same polarity (i.e., orientation) relative to the reference loop $i_1$. In contrast, $V_2$ appears with a negative sign because $V_2$ and $V_{1,eff}$ have opposite polarities relative to the same reference loop $i_1$.

If we kept the other voltage source, $V_2$, we had to replace its value with $$\begin{equation}V_{2,eff}=V_2-V_1\end{equation}$$ (see figure below). In this case, $V_2$ was taken with positive sign because $V_2$ and $V_{2,eff}$ have the same polarity relative to the reference loop $i_1$, while $V_1$ as taken with a negative sign because its polarity is oposite to the polarity of $V_{1,eff}$ relative to the same reference loop $i_1$.

Voltage sources should never be combined in parallel. What would happen if two voltage sources with different voltages are connected in parallel?