What is the intersection between $x + y - z = -2$ and $z^2 = x^2 + y^2$

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I got the answer as $4x + 4y + 2xy + 4 = 0$ by substituting $z = x + y + 2$ into the second equation, but I feel as this is wrong since I am missing $z$ in the function. How do I approach this problem?