Eliminate variables from a three‑equation system

Eliminate $x, y, z$ from the equations $a x + h y + g z = 0, h x + b y + f z = 0, g x + f y + cz = 0$ .

~10 minAnswer checked instantlydeterminantelimination

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 17

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