Results 1 to 3 of 3
Like Tree3Thanks
  • 1 Post By skeeter
  • 2 Post By HallsofIvy

Thread: Need some help with system of equations

  1. #1
    Newbie
    Joined
    Feb 2017
    From
    USA
    Posts
    6

    Need some help with system of equations

    Sorry if this is the wrong sub-forum to post this on, can a admin move if wrong?

    need some help with this system of equations


    find the value of the parameters a and p for which the system


    x + 5y = 6,
    6y + az = a + 1 - p,
    x - ay + z = p + 2


    i. unique solution
    ii. infinitly many solutions
    iii. no solutions
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,043
    Thanks
    3621

    Re: Need some help with system of equations

    go to the link ... scroll down to topic #3 Cramer's Rule - system of three linear equations in three variables

    Solving systems via Cramer's Rule - CATs
    Thanks from zwambooo
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,174
    Thanks
    2815

    Re: Need some help with system of equations

    One way to do this is to try to solve the system. From x+ 5y= 6, x= 6- 5y so x - ay + z = p + 2 becomes 6- 5y- ay+ z= 6- (a+ 5)y+ z= p+ 2 or (a+ 5)y+ z= p- 4. Then z= p- 4- (a+ 5)y. Putting that into 6y+ az= a+ p- 1, we have 6y+ a(p- 4- (a+ 5)y)= 6y- (a^2+ 5a)y+ap- 4a= a+ p- 1 or (a^2+ 5a- 6)y= (a+ 6)(a- 1)y= a+ p- 1- ap+ 4a.

    Now we would like to solve that for y by dividing both sides by (a+ 6)(a- 1). If neither a+ 6 or a- 1 is 0, then we can divide by (a+ 6)(a- 1) and have a unique solution. If is either -6 or 1, then (a+ 6)(a- 1) is 0 the equation becomes 0= a+ p- 1- ap+ 4a. There is no y in that equation but there are still two possibilities. If a+ p- 1+ ap+ 4a is NOT 0 then the equation is untrue for any y. But f a+ p- 1+ ap+ 4a is 0, then the equation is 0 which is always true, for all y.
    Thanks from topsquark and zwambooo
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: Sep 2nd 2015, 04:11 PM
  2. Replies: 1
    Last Post: Jun 10th 2013, 07:59 PM
  3. The system of equations (64 equations -12 unknown) solution help
    Posted in the Math Challenge Problems Forum
    Replies: 0
    Last Post: Jan 17th 2013, 07:28 AM
  4. Replies: 0
    Last Post: Mar 21st 2012, 01:38 AM
  5. Replies: 2
    Last Post: Apr 20th 2010, 03:26 PM

/mathhelpforum @mathhelpforum