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Solve for $\{x,y,z\}$: \begin{cases}\dfrac1x+\dfrac2y-\dfrac1z=\dfrac43\\\\ \dfrac2x+\dfrac3y-\dfrac2z=\dfrac53\\\\ \dfrac3x+\dfrac4y-\dfrac6z=3 \end{cases}

My attempt: I have tried combining each equation like so:$$\frac {yz+2xz-xy}{xyz}=\frac43$$ for each equation, but I got nowhere.

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2 Answers 2

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Why don't you solve for $\frac1x$ and the like, and then just take the inverse?

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  • $\begingroup$ I did not do that because apparently I cannot see simple things like that. Thanks for the answer. Helpful. $\endgroup$ Feb 15, 2016 at 2:53
  • $\begingroup$ You could find useful this: en.wikipedia.org/wiki/How_to_Solve_It. $\endgroup$
    – Chip
    Feb 15, 2016 at 2:56
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Take $x_1=\frac1x, y_1=\frac1y, z_1=\frac1z$

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