# System of Equations

**Algebra**Level pending

\[ \begin{cases} y+z = cx \\ x +z = cy \\ x+y = cz \end{cases} \]

For which **non-zero** values \(c\in \mathbb{R}\) does the system of equations above have a solution \((x,y,z) \in \mathbb{R}^3\)?

\[ \begin{cases} y+z = cx \\ x +z = cy \\ x+y = cz \end{cases} \]

For which **non-zero** values \(c\in \mathbb{R}\) does the system of equations above have a solution \((x,y,z) \in \mathbb{R}^3\)?

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