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Find all triples (x,y,z)

Source: 1976 AHSME Problem 30

May 19, 2014
AMC

Problem Statement

How many distinct ordered triples (x,y,z)(x,y,z) satisfy the equations \begin{align*}x+2y+4z&=12 \\ xy+4yz+2xz&=22 \\ xyz&=6~~?\end{align*}
<spanclass=′latex−bold′>(A)</span>none<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>4<spanclass=′latex−bold′>(E)</span>6<span class='latex-bold'>(A) </span>\text{none}\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>4\qquad <span class='latex-bold'>(E) </span>6
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