1. Not finding help here? Sign up for a free 30min 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!

Three variable equations

  1. Apr 5, 2014 #1
    1. The problem statement, all variables and given/known data

    find (x,y,z)

    2. Relevant equations

    3x - 4y + 7z = 0,-------------->first equation

    2x - y - 2z = 0,---------------->second equation

    3x3 - y3 + z3 = 18.---->third equation

    3. The attempt at a solution

    on subtracting first two equations i get x - 3y + 9z = 0

    using this if i solve the both first two equations i get 5y - 20z = 0.

    if i add the first 2 equations i get x - y -z =0

    with this equation if i solve the first equation i get y = 10z
    but if i solve 2nd one i get y=0.
     
  2. jcsd
  3. Apr 5, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    The best way is to proceed systematically; it may take a bit longer, but it is helpful in avoiding errors. So, from eq (2) we get ##y = 2x - 2z.## Putting this into equation (1) we have
    [tex] 0 = 3x - 4(2x - 2z) + 7z = -5x +15 z[/tex]
    So, ##x = 15z / 5 = 3z##, and putting this into the expression for y we have ##y = 2(3z) - 2z = 4z##. Now put ##x = 3z, y = 4z## into equation (3).

    Note: we started solving for y in terms of z and z from eq. (2). We could equally well have started by solving for x in terms of y and z from eq. (1), etc., but the expressions would have been a bit more complicated. When in doubt, just forge ahead and do it.
     
  4. Apr 5, 2014 #3

    Mark44

    Staff: Mentor

    smart_worker,
    Merely subtracting one equation from another to get a third equation isn't much help if the new equation still has three variables in it. A better way to go would be to add a multiple of one equation to the other so as to eliminate a variable. For example, you could add (-4) times the second equation to the first to get a new equation in only x and z.

    Ray is suggesting a different approach. Since he has gone into more detail, I'll leave you to follow his suggestion.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted