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System of Equations Involving a Quadratic: Have Answer <> Understand

  1. Dec 11, 2013 #1
    1. The problem statement, all variables and given/known data

    Solve this system of equations for x and y.

    v=x+y
    v^2=x^2+y^2

    2. Relevant equations

    The quadratic formula:

    x = (-b +/- sqrt(b^2-4*a*c))/(2*a)

    3. The attempt at a solution

    A TA gave the following advice:

    "Make y the subject of the first equation.
    Find y2 in terms of v and x using this equation.
    Substitute y2 in the second equation.
    You now have a quadratic equation in x and there will be two solutions"​

    I know the answers are x=0 and y=v but I "can't get there from here." My most recent attempt I got as far as 2x^2-2vx=0.

    In this case, this homework is already solved so if someone could walk me through it I would be grateful.
     
  2. jcsd
  3. Dec 11, 2013 #2

    Mark44

    Staff: Mentor

    I would do something different from what your TA suggested. The first equation is v = x + y. I would substitute substitute x + y for v in the second equation, to get (x + y)2 = x2 + y2.

    Expand the left side and simplify. What do you get?
     
  4. Dec 12, 2013 #3

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    So is your question just how to solve this quadratic equation really? Because you can easily factor it
    2x(x-v) = 0

    So what are the possibly solutions?
     
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