# Danny's system of equations

Algebra Level 3

If $$x,y,$$ and $$z$$ are real numbers that satisfy the following system of equations:

\begin{align} x^2 +6y & = -14 \\ y^2 + 12z &= -63 \\ z^2 - 4x &= 28, \end{align}

what is the value of $$\lvert x + y + z \rvert$$?

This problem is posed by Danny H.

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