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Eliminate one variable from an equation using other equations?

Posted 19 days ago
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Hello, I have a set of functions, lets say x, y, and z. I want to remove a variable (S) from y, while not removing it from the others (I do not care about the possible combinations that do not include all of equation y). The closest command I've encountered is Eliminate. The problem is it then goes and eliminates the same variable from the other equations. I want it to use the information from x and z to make the simplest substitution for the variable in equation y. What would be a fix/command to better suit what I am looking for? Thank you for any and all help.

It is suggested that you provide more detail of your functions, etc. What exactly did you try?

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