line of intersection in planes?

Question

The line of intersection for the 2 planes:
2x-y+2z-3 = 0 and x + 2y -z -1 = 0 is (x, y,z).

Answer 1

step by step
assume x=0
==>-y+2z=3
and 2y-z=1
==>z=7/3 and y=5/3
so we have a point on the intersection.(0,7/3,5/3)
now you need vectors of to plane.
1:(2,-1,2)
2:(1,2,-1)
now multiply these vectors
==>(-3i+4j+5k)
(-3,4,5)
now that you have 1 point of line and the vector of line you can find the formula
x/-3=(y-7/3)/4=(z-5/3)/5

Answer 2

put the two equations to equal each other then solve

2x-y +2z -3 = x +2y - z -1

Answer 3

x-3y+3z=2