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    Quadratic Equation & Vieta Theorem

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    Kindly elaborate on the concept of squared variables in a system of equations by the sample that was given to me. See attached file for full problem description.

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    Solution Preview

    I understand your question as a request on how to deal with this system of equations correctly and with understanding.

    The second equation, xy = 6 has no squares so that x and y are uniquely related.
    We can say y = 6/x and substitute it into the 1st equation:

    x^2 +36/x^2 = 25

    Now we multiply this by x^2, move everything to the left hand side and get

    x^4 - 25 x^2 + 36 = 0

    Formally, this is an equation of the 4th order, but in fact it can be reduced to 2nd order by substitution
    z = ...

    Solution Summary

    The concepts of square variables in a system of equations are found. Square variables are determined.