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Homework Help: 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

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    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


    Staff: Mentor

    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.
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