Question

If X+y+z=2
Xy+xz+yz=-5
X^2 + y^2 + z^2 = 14
Find X, y, and z

Answer 1

If we substitute z = 2 - x - y in the last 2 equations it simplifies to 2 equations in x and y:=

x^2 + y^2 + xy - 2x - 2y = 5 and
-x^2 - y^2 - xy + 2x + 2y = -5

if we add these we get 0 = 0 so there are infinite solutions