How do you solve the system #x+y-2z=5#, #x+2y+z=8#, #2x+3y-z=13#?

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Answer 1 · 2018-03-20T15:03:40

#x=5k+2#, #y=3-3k# and #z=k#

Perform the Gauss Jordan elimination on the augmented matrix

#A=((1,1,-2,|,5),(1,2,1,|,8),(2,3,-1,|,13))#

I have written the equations not in the sequence as in the question in order to get #1# as pivot.

Perform the folowing operations on the rows of the matrix

#R2larrR2-R1#; #R3larrR3-2R1#

#A=((1,1,-2,|,5),(0,1,3,|,3),(0,1,3,|,3))#

Consequently this system has infinite solutions. After choosing #z=k#, #y# must be #3-3k# and #x# must be #5k+2#