ISL 1989 Problem 46

Let S be the point of intersection of the two lines $l_1 : 7x - 5y + 8 = 0$ and $l_2 : 3x + 4y - 13 = 0.$ Let $P = (3, 7), Q = (11, 13),$ and let $A$ and $B$ be points on the line $PQ$ such that $P$ is between $A$ and $Q,$ and $B$ is between $P$ and $Q,$ and such that $$\frac{PA}{AQ} = \frac{PB}{BQ} = \frac{2}{3}.$$ Without finding the coordinates of $B$ find the equations of the lines $SA$ and $SB.$