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: $$V_{eff}=\pm V_1 \pm V_2\pm...\pm V_n$$ where each term on the right-hand side uses a $+$ sign if the corresponding voltage source $V_i$ is oriented in the same direction as $V_{eff}$, and a $-$ sign if it is oriented in the opposite direction. Since the voltage sources are all connected in series, when we replace $V_i$ with $V_{eff}$ the other voltage sources are short-circuited (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 $V_1$, set its value to $$\begin{equation}V_{1,eff}=V_1-V_2\end{equation}$$ 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 (orientation) with respect 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 $V_1$ was taken with a negative sign because its polarity is opposite 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 not be combined in series. What happens if two current sources with different currents are connected 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 each term on the right-hand side uses a $+$ sign if the corresponding current source $I_i$ points toward the same node as $I_{eff}$, and a $-$ sign if it points to the opposite node. Since all 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 $I_1$, and set its value to $$\begin{equation}I_{1,eff}=I_1-I_2+I_3\end{equation}$$ then remove current sources $I_2$ and $I_3$ from the circuit. Notice that $I_1$ and $I_3$ appear with positive signs above because both $I_1$ and $I_3$ point toward node $v_3$, like $I_{1,eff}$. $I_2$ appears with a negative sign because it points toward node $v_4$ while $I_{1,eff}$ points toward node $v_3$. If we kept current source $I_2$, we would set its value to $$\begin{equation}I_{2,eff}=-I_1+I_2-I_3\end{equation}$$ Here $I_1$ and $I_3$ appear with positive signs because $I_2$ points toward node $v_4$, like $I_{2,eff}$. $I_1$ and $I_3$ appear with negative signs because they point toward node $v_3$ while $I_{2,eff}$ points toward node $v_4$. Similarly, if we kept current source $I_3$, we would set its value to $$\begin{equation}I_{3,eff}=I_1-I_2+I_3\end{equation}$$