11x+y-5z=111x+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