SOLUTION: xy+xz=2 yx+yz=2 xz+yz=2

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Question 97919: xy+xz=2
yx+yz=2
xz+yz=2
Answer by aaaaaaaa(138) About Me  (Show Source):
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xy%2Bxz+=+yx%2Byz+=+2%29
cross%28xy%29+%2B+xz+=+cross%28xy%29+%2B+yz
xz+=+yz
x+=+y
xz+%2B+yz+=+xy+%2B+xz+=+2
cross%28xz%29+%2B+yz+=+xy+%2B+cross%28xz%29
yz+=+xy
z+=+x
(with y and z different from 0)
Substitute for y and z in equation 1:
2x%5E2+=+2
x%5E2+=+1
x+=+1 or x+=+-1
x = y = z = +-1