#11x+y-5z=1##..........(i)#
#7x+13y+z=1##............(ii)#
#8x-y-z=11##.............(iii)#
Adding #(ii)# and #(iii)# we get
#15x+12y=12#
#implies 5x+4y=4##..........(iv)#
Multiply #(ii)# by #5# and add in #(i)#
#implies 35x+65y+5z=5#
#and 11x+y-5z=1#
By addition we have
#46x+66y=6#
#implies 23x+33y=3##...............(v)#
Multiply #(iv)# by #33# and #(v)# by #4# and subtract (v) from (iv)
#implies 165x+132y=132#
#and 92x+132y=12#
By subtraction we have
#73x=120#
#implies x=120/73#
Put #x=120/73# in #(iv)#
#implies 5(120/73)+4y=4#
#implies 600+292y=292#
#implies 292y=-308#
#implies y=-308/292=-77/73#
#implies y=-77/73#
Put #x=120/73# and #y=-77/73# in #(iii)#
#implies 8(120/73)-(-77/73)-z=11#
#implies z=8*120/73+77/73-11#
#implies z=960/73+77/73-11=(960+77-803)/73=234/73#
#implies z=234/73#
