Extremely hard algebra!

  1. 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. jcsd
  3. VietDao29

    VietDao29 1,422
    Homework Helper

    [tex]\left\{ \begin{array}{l} -x ^ 2 - 2xy + 12 = 0 \ \ (1) & -y ^ 2 - 2xy + 12 = 0 \ \ (2) \end{array} \right.[/tex]
    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
    [tex]\Leftrightarrow \left[ \begin{array}{l} x = y & x = -y \end{array} \right.[/tex]
    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
  4. VietDao29

    VietDao29 1,422
    Homework Helper

    No complete solution, please!!! :grumpy:
    We all know how intelligent you are!!!
    Read this!!!
    :grumpy:
    Read line #9!!!
     
  5. benorin

    benorin 1,026
    Homework Helper

    Line #9!!! My bad. :uhh:
     
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