solve the following for u and t
x= u + t^2
y = t - u^2
you are right what you are doing.
after you simplfy you get:
$\displaystyle y=t-x^2+2t^2x-t^4$
well we need to rearrange it a little bit, so we get:
$\displaystyle y=-x^2+2t^2x+(t-t^4)$
then using the Quadratic equation
we sub in the numbers,
$\displaystyle \frac{-2t^2\pm\sqrt{(2t^2)^2-4*-1*(t-t^4)}}{2*-1}=0$
then again simplfy:
$\displaystyle \frac{-2t^2\pm\sqrt{4t}}{-2}=0$
so we get t=1 or t=0
if t=0 x=0
if t=1 x=2 or 0.
hope this helps. correct me if im wrong anyone.
You can simplify even further, Babymilo :
$\displaystyle \frac{-2t^2\pm\sqrt{4t}}{-2}=0$
Extract the $\displaystyle 4$ from the square root :
$\displaystyle \frac{-2t^2\pm 2 \sqrt{t}}{-2}=0$
Factorize $\displaystyle 2$ :
$\displaystyle \frac{2(-t^2 \pm \sqrt{t})}{-2}=0$
Cancel out the $\displaystyle 2$ :
$\displaystyle \frac{-t^2 \pm \sqrt{t}}{-1}=0$
Finally :
$\displaystyle t^2 \mp \sqrt{t} = 0$