How do you solve the system of equations #x- y + 2z = 9#, #- 2x + y + z = - 1#, and #2x + 2y - z = - 5#?

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Answer 1 · 2017-06-28T13:18:50

#"solution "(1,-2,3)#

we can solve by elimination

we have:

#x-y+2z=9----(1)#

#-2x+y+z=-1 ---(2)#

#2x+2y-z=-5---(3)#

#(2)+(3)" "#eliminates #" "x" "#&#" "z#

#=>3y=-6#

#:.color(red)(y=-2)#

using #(1)" & "(2)" "#and substituting for#" "y#

#x+2+2z=9#

#=>x+2z=7---(1a)#

#-2x-2+z=-1#

#=>-2x+z=1--(2a)#

#(1a)xx2#

#2x+4z=14--(1b)#

#(2a)+(1b)" eliminates " x#

#=>5z=15#

#:.color(red)(z=3)#

substitute into #(1a)#

#x+2xx3=7#

#=>color(red)(x=1)#

#"solution "(1,-2,3)#

the verification for consistency is left for the reader as an exercise.