Chapter 12 - Vectors and the Geometry of Space - 12.5 Equations of Lines and Planes - 12.5 Exercises - Page 872: 59

$x=1,y-2=-z$

Given: $5x-2y-2z=1$ and $4x+y+z=6$ Here, $(x_0,y_0,z_0)=(1,1,1)$ and $ \lt a,b,c\gt=\lt 0,-13,13\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: $x=1,y-2=-z$