6. $S$ is the intersection point of the lines $l_{1}: 7 x+5 y+8=0$ and $l_{2}: 3 x+4 y-13=0$. The line passing through points $P(3,7)$ and $Q(11,13)$ has two points $A, B$, where $P$ is between $A$ and $Q$, and $B$ is between $P$ and $Q$, and $\left|\frac{P A}{A Q}\right|=\left|\frac{P B}{B Q}\right|=\frac{2}{3}$. Without finding the coordinates of $S$, find the equations of the lines $S A$ and $S B$.
6. Obviously, point $A$ is the external division point of $P$ and $Q$, $\cdot \frac{PA}{AQ}=-\frac{2}{3}$, then by the section formula we get $x_{A}=$ $-13, y_{1}=-5$.

Similarly, $B$ is the internal division point of $P$ and $Q$, $\frac{PB}{BQ}=\frac{2}{3}$, then by the section formula we get $x_{B}=\frac{31}{5}, y_{B}$ $=\frac{47}{5}$.
Therefore, $SA$ and $SB$ are both lines in the line system $7 x-5 y+8+u(3 x+4 y-13)=0$.
Substituting the coordinates of point $A$ into the line system equation gives $u_{2}=\frac{-11}{108}$, hence the equation of $SB$ is $723 x-$ $584 y+1007=0$.