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)
[ 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.