# Math Help - Find x(u,v) and y(u,v) .

1. ## Find x(u,v) and y(u,v) .

given
u=y-x
v=xy

Find x(u,v) and y(u,v) .

Thank you.

2. Originally Posted by kittycat
given
u=y-x
v=xy

Find x(u,v) and y(u,v) .

Thank you.
Use substitution:
$y = u + x$

Thus
$v = x(u + x)$

$x^2 + ux - v = 0$

So
$x = \frac{-u \pm \sqrt{u^2 + 4v}}{2}$

Thus
$y = u + \frac{-u \pm \sqrt{u^2 + 4v}}{2} = \frac{u \pm \sqrt{u^2 + 4v}}{2}$

Which of the "+" or "-" signs to use is going to depend on the specific nature of the problem where the u and v come from. At this stage all we can say is that there are two acceptable solutions.

-Dan