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Which is true?

Algebra Level 1

$\large { \begin{aligned} x&=&y^a \\ y&=&z^b \\ z&=&x^c \end{aligned}}$

If $x,y$ and $z$ satisfy the system of equations above, which one of the following is true?

a - b - c = 1

abc = 1

ac + b = 1

a + b + c = 1

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by Anish Harsha

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