# Symmetric System of Equations

**Algebra**Level 4

Find the number of real solutions of the system of equations.

\[\left\{ \begin{array}{l} x^2-y^2=z,\\ y^2-z^2=x,\\ z^2-x^2=y. \end{array} \right.\]

Find the number of real solutions of the system of equations.

\[\left\{ \begin{array}{l} x^2-y^2=z,\\ y^2-z^2=x,\\ z^2-x^2=y. \end{array} \right.\]

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