* problem*: Consider the following simultaneous equations in x and y :

where is a real constant. Show that these equations admit real solutions in x and y.

* solution*: … (i)

… (ii)

[ replacing x in terms of y. ]

This is a 3rd degree polynomial over y.

Now as we know any odd degree polynomial has at least one real root.That is why y has also at least one real root.Now for that particular root we get also real.

*Conclusion*: & admits real solutions in x and y.