Superflous Symbols

Algebra Level 3

x(x+y+z)=26y(x+y+z)=27z(x+y+z)=28 \begin{array}{c} x(x+y+z)=26 \\ y(x+y+z)=27 \\z(x+y+z)=28 \end{array}

How many triplets of real numbers (x,y,z)(x,y,z) satisfy the system of equations above?

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