Question

|{ -x+2y+2z=0
<|{ -x-2y-2z=0
|{ x -z=-1

possible answers are
(0,1,1)
(-1,-1,-1)
(0,-1,-1)
(0,-1,1)

Answer 1

i think it is easier to check than to solve. but maybe not

Answer 2

add the first to equations together and you get -2x=0 which means x = 0 and we can eliminate choice 2

Answer 3

since x=0 the third equation says -z=-1 making z=1 and we can eliminate choice 3

Answer 4

now we know z = 1 and x = 0 so first equation says
\[2y=0(1)=0\] \[2y+2=0\]
\[2y=-2\]
\[y=-1\]
so it is the last one (0,-1,1)

Answer 5

clear or no?

Answer 6

i tried to plug them in but that -(- was bothering me but i understand

Answer 7

easy to see that if you add the first two equations both the y and z drop out so you can solve for x easily

Answer 8

yeah i get it

Answer 9

another?