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?

Current sources should never be combined in series. What would happen if we connect two current sources with different currents in series?

If two or more current sources $I_1$, $I_2$, ... $I_n$ are connected in parallel they can be replaced with a single current source with $$I_{eff}=\pm I_1 \pm I_2\pm...\pm I_n$$ where the terms in the right-hand side are taken with $+$ sign if the corresponding current source $I_i$ points towards the same node as $I_{eff}$ and with $-$ sign if $I_i$ points to the other node. Since all the current sources are connected in parallel, when we replace $I_i$ with $I_{eff}$, the other current sources are removed (i.e. replaced with open circuits).

For instance, consider the circuit in Fig. 2, in which current sources $I_1$, $I_2$, and $I_3$ are connected in parallel. In this circuit, we can keep one current source, say $I_1$, replace its value with $$\begin{equation}I_{1,eff}=I_1-I_2+I_3\end{equation}$$ and remove current sources $I_2$ and $I_3$ from the circuit. Notice that $I_1$ and $I_3$ appear with positive sign in the above equation because both $I_1$ and $I_3$ point towards node $v_3$, just like $I_{1,eff}$. $I_2$ appears with negative sign because it points towards node $v_4$ while $I_{1,eff}$ points towards node $v_3$. If we kept current source $I_2$, we had to replace its value with $$\begin{equation}I_{2,eff}=-I_1+I_2-I_3\end{equation}$$ $I_1$ and $I_3$ appear with positive sign in the above equation because $I_2$ points towards node $v_4$, just like $I_{2,eff}$. $I_1$ and $I_3$ appear with negative sign because they point towards node $v_3$ while $I_{2,eff}$ points towards node $v_4$. Also, if we kept current source $I_3$, we had to replace its value with $$\begin{equation}I_{3,eff}=I_1-I_2+I_3\end{equation}$$