[tex] \it x \cdot y = 6 \Rightarrow x = \dfrac{6}{y} \\ y \cdot z=21 \Rightarrow z= \dfrac{21}{y} \\ \\ x \cdot z = 14 \Rightarrow \dfrac{6}{y} \cdot \dfrac{21}{y} = 14 \Rightarrow \dfrac{6 \cdot 21}{y^{2}}=14 \Rightarrow 6 \cdot 21 = 14 \cdot y^{2} \Rightarrow 2 \cdot 3 \cdot 3 \cdot 7 = 2 \cdot 7 \cdot y^{2} \Rightarrow y^{2} = 3 \cdot 3 \Rightarrow y^{2} = 3^{2} \Rightarrow \boxed{y=3} \\ \\ x= \dfrac{6}{3} \Rightarrow \boxed{x=2} \\ z= \dfrac{21}{3} \Rightarrow \boxed{z=7} [/tex]
