## Solving a system in terms of intersecting planes

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?
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 Recognitions: Gold Member Science Advisor Staff Emeritus 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?
 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.