How do you solve the following system?:# 11x+y-5z=1, 7x+13y+z=1, 8x-y-z=11#

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Answer 1 · 2015-12-29T20:48:28

#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#