How do you solve the system of equations #5x + 13y + z = 89#, #- 2x - 6y - z = - 44#, and #7x + 14y + z = 97#?

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Answer 1 · 2018-01-11T03:24:52

#x=4/11#, #y=69/11# and #z=62/11#

#(5x+13y+z)+(-2x-6y-z)=89-44# or #3x+7y=45#

#(-2x-6y-z)+(7x+14y+z)=-44+97# or #5x+8y=52#

#5*(3x+7y)-3*(5x+8y)=5*45-3*52#

#15x+35y-15x-24y=225-156#

#11y=69#, so #y=69/11#

Hence,

#3x+7*69/11=45#

#3x+483/11=45#

#3x=12/11#, so #x=4/11#

Thus,

#-2*4/11-6*69/11-z=-44#

#-z-422/11=-44#

#-z=-62/11#, so #z=62/11#