# Math Help - Planes Point of Intersection

1. ## Planes Point of Intersection

a)Determine the equation of the line of intersection L between the planes pi1: 2x+3y-z=3 and pi2: -x+y+z=1.

b) Determine the point of intersection between L and the xz-plane.

I need help with part b)

for part a) my answer is: z=t, x=4t/5, and y=1- (t/5)
which is correct.
now for part b) my work thus far is:

(x,y,z)=(0,0,0)+t(0,1,0) <<< xz-plane means y-axis

i substituted the parametric equations into symmetric equations

and I ended up with t=0, then i substituted t=0 into the parametric equation.

My answer doesn't match the back of the book, can someone tell me what I did wrong. Explain the correct method. Thanks!

2. The plane $y=0$ is the $xz\text{plane}$.
So I get $t=5$.