Solve the system of equations: \( \left.\begin{array}{l}z+a y+a^{2} x+a^{3}=0 \\ z+b y+b^{2} x+b...

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Solve the system of equations: \( \left.\begin{array}{l}z+a y+a^{2} x+a^{3}=0 \\ z+b y+b^{2} x+b^{3}=0 \\ z+c y+c^{2} x+c^{3}=0\end{array}\right] \) where \( a \neq b \neq c \).
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