Question 886137
Put into matrix form and use elementary row operations to convert into an upper triangular  arrangement.


{{{(matrix(3,4,2,-1,-1,1,1,2,1,0,3,-1,-2,-1))}}}


{{{(matrix(3,4,1,2,1,0,2,-1,-1,1,3,-1,-2,-1))}}}


{{{(matrix(3,4,1,2,1,0,0,-5,-3,1,0,-7,-5,-1))}}}, R2-2*R1, R3-3*R1


{{{((matrix(3,4,1,2,1,0,0,5,3,1,0,7,5,1)))}}}, multiply row 2 and 3 by -1


{{{((matrix(3,4,1,2,1,0,0,35,21,7,0,35,25,5)))}}}, 7*R2, 5*R3



{{{(matrix(3,4,1,2,1,0,0,5,3,1,0,0,2,1))}}}, (1/7)R2, (1/2)R3


This can continue using subtraction to eliminate elements above the diagonal.  This is already in a form that says, {{{z=-1/2}}}, and you can use this to back substitute and solve for the next variables one at a time.


{{{(matrix(3,4,1,2,1,0,0,5,3,1,0,0,1,-1/2))}}}, R3 divid by 2


{{{(matrix(3,4,1,2,0,1/2,0,5,0,5/2,0,0,1,-1/2))}}}, R2-3R3, R1-R3


{{{(matrix(3,4,1,2,0,1/2,0,1,0,1/2,0,0,1,-1/2))}}}, Divide R2 by 5


And next do R1-2*R2, ...  and your matrix tells you the solution.


After so much long, detailed work, I believe I see a mistake...
hopefully you can understand the process being shown and can check and reduce the matrix on paper and be sure of the correct answers.


REDONE ON PAPER:
Tracing the work between paper and the (wrongly) posted solution is difficult.  Let me just post here my redone RESULT solution matrix; likely some of the arithmetic computation was wrong in computing one of the elements.
This one should be right...
{{{(matrix(3,4,1,0,0,2/11,0,1,-5/11,0,0,1,12/11))}}}
---
Rendering is failing at the moment.
{{{x=2/11}}}
{{{y=-7/11}}}
{{{z=12/11}}}