Linear and cubic equations with a sum condition

Solve the system
$x + y = z,$
$3 x - 2 y + 17 z = 0,$
$x^{3} + 3 y^{3} + 2 z^{3} = 167.$

~10 minAnswer checked instantlysubstitutioncubic equation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 21

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).