This problem was confusing me so any help would be appreciated!
Write both the parametric and symmetric equations of the line of intersection of the planes with the equations 2x - y + z = 5 and x + y - z = 1.
Thus, we have that this line must contains the points
Thus, the Symettric Equation is:
Note, this is a zero in the denominator of the first fraction, it is a useful notation I saw in a Russian Textbook* which simply means constantly, so it is just a shorthand notation.
*)If you are interested the Textbook was written by Perelman! Not Perelman you think it is but his grandfather!
This is how I was taught to find the intersection of two planes.Write both the parametric and symmetric equations of the line of intersection
of the planes with the equations: .
We have: .
Add  and : .
Substitute into : .
We have as a function of
On the right side, replace with a parameter .
. . . . . . . . There!