Explanation

(b)
The family of lines
$(x + y - 1) + \lambda(2x + 3y - 5) = 0$
passes through a point such that
$x + y - 1 = 0$
$2x + 3y - 5 = 0$
$ie,\ ( - 2,\ 3)$ and family of lines
$(3x + 2y - 4) + \mu(x + 2y - 6) = 0$
Passes through a point such that
$3x + 2y - 4 = 0$
and $x + 2y - 6 = 0\ ie,\ ( - 1,\ 7/2)$
$\therefore$ Equation of the straight line that belongs to both the families passes through $( - 2,\ 3)$ and $( - 1,\ 7/2)$ is
$y - 3 = \frac{\frac{7}{2} - 3}{- 1 + 2}(x + 2)$
$\Rightarrow y - 3 = \frac{x + 2}{2} \Rightarrow x - 2y + 8 = 0$