What is the solution to the following system? x+y+z=6 x-y+z=8 x-y-z=0

(6,-1,1)

Step-by-step explanation:

First pair two of the equations together twice:

I chose x+y+z=6 and x-y+z=8

Used the elimination method and eliminated the y's and got x+z=7

Then I took another pair of equations x+y+z=6 and x-y-z=0

Using the elimination method I once again eliminated the y's (and z's) and got x=6

I then plugged x=6 into x+z=7 and got that z=1

I then plugged x=6 and z=1 into the original equation x+y+z and got y=-1

Thus, x=6 7=-1 z=1 and in coordinate form (6,-1,1).