Solving a system in terms of intersecting planes

Tonyt88

1. The problem statement, all variables and given/known data

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


2. Relevant equations



3. 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.