1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Problem solving equation system

  1. Oct 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve this equation system for x, y and lambda.

    2x = \lambda (2x-6y)\\
    2y = \lambda(-6x-14y)\\

    3. The attempt at a solution

    I really tried A LOT of things, but I can't solve it. I think it is not helpful to post here all the arithmetic ways I tried.

    Thank you for the help!
  2. jcsd
  3. Oct 8, 2012 #2


    User Avatar
    Homework Helper

    Can you just explain what you've tried so far?
  4. Oct 9, 2012 #3
    Thank you for your response, rcgldr.

    I have tried simple substitution. Tried to come up with one equation of one variable from substituting, summing and manipulating the system's equations. But I could not get an equation of one variable, at least with the substitutions I tried.

    I don't know if this helps, but the real problem is to find the distance from the curve to the origin. The curve is the last equation in the system. So I'm using Lagrange where the distance equation if the f(x,y) and the curve equation is the g(x,y). This system came up from gradient(x^2 + y^2) = Lambda * gradient(x^2 - 6xy -7y^2 + 80).
  5. Oct 9, 2012 #4


    User Avatar
    Homework Helper

    Isolate y from the first equation and substitute into the second. What do you get?

  6. Oct 9, 2012 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You can solve the first equation for x in terms of y and λ (although not for some, special values of λ---they would need separate treatment). Substituting that into the second equation gives you an equation of the form y*A(λ) = 0, so either y = 0 or A(λ) = 0.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook