|{ -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)

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|{ -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)

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i think it is easier to check than to solve. but maybe not
add the first to equations together and you get -2x=0 which means x = 0 and we can eliminate choice 2
since x=0 the third equation says -z=-1 making z=1 and we can eliminate choice 3

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Other answers:

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)
clear or no?
i tried to plug them in but that -(- was bothering me but i understand
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
yeah i get it
another?

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