Extremely hard algebra!

1. Nov 8, 2005

dagg3r

hi this is a hard algebra qestion
i have these 2 formulas

12-x^2 -2xy = 0
12-y^2 - 2xy = 0

for some reason x and y are both 2

how do you get this
i tried and got

y= 6/x -0.5x tried to sub into second one but gets messy any way to do this on a calculator by any chance i have a Ti-83 but i want to know how to do it algebraically

thanks!

2. Nov 8, 2005

VietDao29

$$\left\{ \begin{array}{l} -x ^ 2 - 2xy + 12 = 0 \ \ (1) & -y ^ 2 - 2xy + 12 = 0 \ \ (2) \end{array} \right.$$
You should note that there are 12, and -2xy in both (1), and (2), so it's common to subtract both sides of (1) from both sides of (2), or to subtract both sides of (2) from both sides of (1).
So (1) - (2) gives:
y2 - x2 = 0
$$\Leftrightarrow \left[ \begin{array}{l} x = y & x = -y \end{array} \right.$$
So you have 2 cases: x = y and x = -y.
Case 1: x = y,
substitute that back to either (1) or (2), to solve for y, then for x (in this case x = y).
Case 2: x = -y,
substitute that back to either (1) or (2), to solve for y, then for x (in this case x = -y).
Can you go from here?

Last edited: Nov 8, 2005
3. Nov 8, 2005

VietDao29

We all know how intelligent you are!!!
:grumpy:

4. Nov 8, 2005