Answer
$\frac{x}{2}=\frac{y}{-1}=\frac{z+5}{5}$
or:
$\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z}{5}$
Work Step by Step
Given: $z=2x-y-5$ and $z=4x+3y-5$
Here, $(x_0,y_0,z_0)=(0,0,-5)$ and $\lt a,b,c\gt=\lt 4,-2,10\gt$
The symmetric equations are defined by:
$\frac{x-x_0}{a}=\frac{y-y_0}{b}=\frac{z-z_0}{c}$
Hence, the symmetric equations are:
$\frac{x}{2}=\frac{y}{-1}=\frac{z+5}{5}$
or:
$\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z}{5}$
