Chapter 12 - Vectors and the Geometry of Space - 12.5 Equations of Lines and Planes - 12.5 Exercises - Page 872: 60

$\frac{x}{2}=\frac{y}{-1}=\frac{z+5}{5}$

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: $\frac{x}{2}=\frac{y}{-1}=\frac{z+5}{5}$