Can someone help me solve this systems of equations problem using a matrix and in reduced row echelon form:

3x-y+z=10

2x-4y-z=20

6x+8y+z=-100

i got the answers to be x: -6, y=-8, and z=0

i need help,though, on how to complete this problem without a calculator, like a walk through. any help would be greatly appreciated

i have it set up here