The symmetrical form of the line of intersection of the planes x = ay…

$x = ay + b,\quad z = cy + d$

$y = \lambda$

$x = a\lambda + b,\quad z = c\lambda + d$

$\text{Direction ratios} = (a, 1, c)$

$\text{Point on line} = (b, 0, d)$

$\frac{x - b}{a} = \frac{y - 0}{1} = \frac{z - d}{c}$

The symmetric form is $\frac{x - b}{a} = \frac{y}{1} = \frac{z - d}{c}$.