Explanation

(b)
Given lines are $3x + 4y = 5,\ 5x + 4y = 4$ and $\lambda x + 4y = 6$. These three lines meet at point, if the point of intersection of first two lines lies on the third line
Now, point of intersection of line $3x + 4y = 5$ and $5x + 4y = 4\ is\ \left( - \frac{1}{2},\frac{13}{8} \right)$
The line $\lambda x + 4y = 6$ passes through the point $\left( - \frac{1}{2},\frac{13}{8} \right)$
$\therefore\ \lambda\left( - \frac{1}{2} \right) + 4\left( \frac{13}{8} \right) = 6$
$\Rightarrow - \lambda + 13 = 12$
$\Rightarrow \ \lambda = 1$