How do you solve the following system?:# x+3y-z=1, 7x+y+z=1, 4x-2y-z=11#

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Answer 1 · 2017-10-28T19:30:20

#x=25/26#, #y=-37/26# and #z=-56/13#

After summing first 2 equations for removing #z#

#x+3y-z+7z+y+z=1+1# or #8x+4y=2#

After summing second and third ones for removing #z#

#7x+y+z+4x-2y-z=1+11# or #11x-y=12#

Now, I removed #y# term from them. I also found #x#

#4*(11x-y)+8x+4y=4*12+2#

#52x=50#, so #x=25/26#

Now, I found #y# from first one.

#8*25/26+4y=2# or #4y=-74/13#, hence #y=-37/26#

Now, I found #z# from third one.

#4*25/26-2*(-37/26)-z=11#

#50/13+37/13-z=11#

#z=87/13-11=-56/13#