Variable z has been eliminated from the equation. For any values we find for x and y that satisfy the equation that is left, there is no restriction on the value of z.
So z = any number
Not a very interesting problem. Are you sure you posted it correctly?
You can put this solution on YOUR website! x+y+z=-x^2-y^2+z
z=..?
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x+y = -x^2-y^2
x = -1
y = 0
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And 0,0
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z = any value, with restrictions on x & y