Solving a system in terms of intersecting planes

[Tonyt88]

Homework Statement

x + 4y + z = 0
4x + 13y + 7z = 0
7x + 22y + 13z = 1

Homework Equations

The Attempt at a Solution

x + 4y + z = 0
- 3y + 3z = 0
-6y + 6z = 1

x + 4y + z = 0
-y + z = 0
-6y + 6z = 1

Then whichever way I solve it I have 0=1 or 0=1/6, so where to go from here or is there just no solution?

 

[HallsofIvy]

First of all, the problem statement is NOT just
x + 4y + z = 0
4x + 13y + 7z = 0
7x + 22y + 13z = 1

That's not a "problem", that's a system of equations. What are asked to do with them?

 

[Tonyt88]

Sorry I had only put it in the title of the thread.

Find all solutions of the linear system. Describe your solution in terms of intersecting planes.