can you guys please classify the system as consinent or inconsitent, and determin solution

x-y+z=6
7x-2y-2z=1
5x+6y+3z=11

double the first, then add to the 2nd----> 9x - 4y = 13 (#4)

triple the first, subtract from 3rd ---> -2x -9y = 7 (#5)

#4 times 2 --> 18x - 8y = 26
#5 times 9 --> -18x -81y = 63
add them
-89y = 89
y = -1

sub into #4
9x + 4 = 13
9x = 9
x = 1

sub into 1st
1 + 1 + z = 6
z = 4

x=1, y = -1, z = 4