line of intersection of the planes

[mathstresser]

What is the line of the intersection of the planes x+y+z=1 and x+z=0?

I get that y=1 and x=-z or x=z=0

so I come up with j, but is that really the answer?

How do I make it a parametric equation and a symmetric equation?

 

[soroban]

Hello, mathstresser!

What is the line of the intersection of the planes x + y + z = 1 and x + z = 0 ?

Start by trying to solve the system of equations: \(\displaystyle \,\begin{array}{cc}x\,+\,y\,+\,z\:=\:1\\ x\,+\,z\:=\:0\end{array}\)
Subtract the equations and we get: \(\displaystyle \,y\,=\,1\)
We also have: \(\displaystyle \,z\,=\,-x\)

So we have: \(\displaystyle \,\begin{array}{ccc}x\,=\,x \\ y\,=\,1 \\ z\,=\,-x\end{array}\)

On the right side, replace \(\displaystyle x\) with a parameter \(\displaystyle t\)

Then we have: \(\displaystyle \,\begin{array}{ccc}x\,=\,t\\y\,=\,1\\z\,=\,-t\end{array}\;\;\) . . . There!