Results 1 to 7 of 7

Math Help - Systems of Linear Equations

  1. #1
    Banned
    Joined
    Oct 2009
    Posts
    39
    Thanks
    1

    Systems of Linear Equations

    Hello all,

    i am studding linear Algrabra from my finals in about 5 days :-)

    I have 2 systems that i dont know exactly how to solve them. Would any1 like to help me solve them ?

    I'd like step by step solution if its possible

    the 1st system is this one:

    dx+y+z=a
    x+dy+z=b
    x+y+dz=c

    where a,b,c Real Numbers


    The Second is this one:

    ax+by+z=1
    x+aby+z=b
    x+by+az=1
    Where a,b Real Numbers


    Please DONT solve them both, just one of them,
    so i ll try the second on my own and then i ll post my
    solution, so you can correct my mistakes

    Thanks alot in advance for your help people , its really important :-)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: Systems of Linear Equations

    Quote Originally Posted by primeimplicant View Post
    Hello all,

    i am studding linear Algrabra from my finals in about 5 days :-)

    I have 2 systems that i dont know exactly how to solve them. Would any1 like to help me solve them ?

    I'd like step by step solution if its possible

    the 1st system is this one:

    dx+y+z=a
    x+dy+z=b
    x+y+dz=c

    where a,b,c Real Numbers


    The Second is this one:

    ax+by+z=1
    x+aby+z=b
    x+by+az=1
    Where a,b Real Numbers


    Please DONT solve them both, just one of them,
    so i ll try the second on my own and then i ll post my
    solution, so you can correct my mistakes

    Thanks alot in advance for your help people , its really important :-)
    dx+y+z=a
    x+dy+z=b
    x+y+dz=c


    z=a-y-dy

    Put this z into
    x+dy+z=b
    x+y+dz=c

    And solve system of 2 equations with 2 variables.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Oct 2009
    Posts
    39
    Thanks
    1

    Re: Systems of Linear Equations

    Quote Originally Posted by Also sprach Zarathustra View Post
    dx+y+z=a
    x+dy+z=b
    x+y+dz=c


    z=a-y-dy

    Put this z into
    x+dy+z=b
    x+y+dz=c

    And solve system of 2 equations with 2 variables.
    hmmm you actually mean z=a-y-dx Right ?

    Isnt it quite easy mode that way ?

    Isnt there any more complex way to solve this ?

    Would you like to give me some solution, the way you would do this? =/

    Thanks again for your help
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: Systems of Linear Equations

    Quote Originally Posted by primeimplicant View Post
    hmmm you actually mean z=a-y-dx Right ?

    Isnt it quite easy mode that way ?

    Isnt there any more complex way to solve this ?

    Would you like to give me some solution, the way you would do this? =/

    Thanks again for your help
    Yes!

    Yes!

    Yes! But way to complex things?

    I gave you.


    You also can solved it with Cramer's rule - Wikipedia, the free encyclopedia.


    Good-luck!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Banned
    Joined
    Oct 2009
    Posts
    39
    Thanks
    1

    Re: Systems of Linear Equations

    Hello again, i solved the first expample in Wikipedia correctly, but i have big trouble in sovling this one, that is more abstract (i mean without numbers). This d, is really confusing me, and theres no inidication if its a real number or something...

    here is what i have done so far





    ill try now the second equation


    edit:

    Alright i stuck on second as well -.-

    this is what ive done so far, i might be tired and cant see the obvious... unlsess is something else tha requires more knowledge.... tips ?
    Last edited by primeimplicant; June 14th 2011 at 03:06 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,596
    Thanks
    1421

    Re: Systems of Linear Equations

    ax+by+z=1
    x+aby+z=b
    x+by+az=1

    If you subtract the first equation from the second you eliminate z: (1- a)x+ (ab-b)y= b-1.

    If you subtract a times the first equation from the third equation you also eliminate z: (1-a^2)x+ (b- ab)y= 1- a

    Note that b-ab= -(ab-b) so if you add those two equations, you eliminate y: (1- a^2+ 1- a)x= b-1+ 1- a or
    (a^2+ a- 2)x= a- b.

    Can you finish that?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Banned
    Joined
    Oct 2009
    Posts
    39
    Thanks
    1

    Re: Systems of Linear Equations

    Quote Originally Posted by HallsofIvy View Post
    ax+by+z=1
    x+aby+z=b
    x+by+az=1

    If you subtract the first equation from the second you eliminate z: (1- a)x+ (ab-b)y= b-1.

    If you subtract a times the first equation from the third equation you also eliminate z: (1-a^2)x+ (b- ab)y= 1- a

    Note that b-ab= -(ab-b) so if you add those two equations, you eliminate y: (1- a^2+ 1- a)x= b-1+ 1- a or
    (a^2+ a- 2)x= a- b.

    Can you finish that?
    thanks for your help, ill try finish this
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Systems of Linear Equations
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 15th 2013, 09:54 PM
  2. Replies: 6
    Last Post: November 30th 2011, 01:41 AM
  3. Systems of Linear Equations
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 12th 2009, 02:00 AM
  4. Replies: 7
    Last Post: August 30th 2009, 10:03 AM
  5. Systems of Linear Equations
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 10th 2008, 07:02 PM

Search Tags


/mathhelpforum @mathhelpforum