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Real solutions (Tomato subjective 71)

problem: Consider the following simultaneous equations in x and y :
\({\displaystyle{4x + y + axy = a}} \)
\({\displaystyle{x – 2y -xy^2 = 0}} \)
where \({\displaystyle{a}} \) is a real constant. Show that these equations admit real solutions in x and y.

solution: \({\displaystyle{4x + y + axy = a}} \)          …  (i)
\({\displaystyle{x – 2y -xy^2 = 0}} \)           … (ii)
\({\displaystyle{x – 2y -xy^2 = 0}} \)
\({\Rightarrow} \) \({\displaystyle{x = {\frac{2y}{1-y^2}}}} \)
\({\displaystyle{x + y + axy = a}} \)

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September 25, 2015

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