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I want to know how to express $a$ in terms of $x$, $y$ and $z$ in the following system (i.e., I want to find the function $a(x,y,z)$). And how to investigate (and to play with the equations) to know whether a variable can expressed in terms of $x, y, z$ or not in similar situations?

$$\begin{cases} x + 2y -z = 2\\ 2x + 5y -(a+2)z = 3\\ -x + (a+5)y + z = 1 \end{cases}$$

P.S.: I would enjoy the solutions written in Maple or Mathematica format too.

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    I think you may want to express $x,y$ and $z$ in terms of $a$. If you still insist in doing it the other way around, solving the problem like an ordinary linear system in the unknown variables $x,y$ and $z$ is still the way to go. You can always invert the relationships afterward if necessary.2011-03-24
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    The try the following link. You'll have to copy the rest of the line into your browser: http://www.wolframalpha.com/input/?i=solve+x%2B2y-z%3D2%2C+2x%2B5y−%28a%2B2%29z%3D3%2C+−x%2B%28a%2B5%29y%2Bz%3D1++for+a2011-03-24
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    Here's @lhf's link in a single clickable version: http://wolframalpha.com/input/?i=solve+x%2B2y-z%3D2%2C+2x%2B5y%2D%28a%2B2%29z%3D3%2C+%2Dx%2B%28a%2B5%29y%2Bz%3D1++for+a2011-03-24
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    @Theo, thanks. How did you do it?2011-03-24
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    @lhf: I tweaked the link using percent encoding (I replaced two or three `-` signs by `%2D`), see http://en.wikipedia.org/wiki/Percent-encoding for an explanation. You can test if a link works in an answer field and wherever the link breaks in the preview you need to do something.2011-03-24

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