Results 1 to 3 of 3

Math Help - System of equations

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    54

    Post System of equations

    Dear Forum I am having issues with the following question any feedback would be appreciated.

    "Describe all possible outcomes of solving a system of two equations. Give examples"

    Thanks -AC-
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,713
    Thanks
    632
    Hello, AlgebraicallyChallenged!

    I would have assumed that you've run into these cases by now.


    Describe all possible outcomes of solving a system of two equations.
    Give examples.
    There are three possible outcomes.



    [1] The system has a unique solution.

    Example: . \begin{array}{ccc}x + y &=& 8 \\ x - y &=& 2\end{array}

    The solution is: . (x,y) \,=\,(5,3)


    The problem asks for two numbers whose sum is 8 and whose difference is 2.
    . . The numbers are 5 and 3.

    If we graph the two lines, they intersect at (5,3).



    [2] The system has no solutions.

    Example: . \begin{array}{ccc}x + y &=& 4 \\ x + y &=& 3\end{array}


    If we try to solve the system, we get a false statement, like: . 0 = 1
    . . This indicates that the system has no solution.


    The problem asks for two numbers whose sum is 4 and whose sum is 3.
    . . Of course, there are no such numbers.

    If we graph the two line, we find that they are parallel.
    . . They do not intersect.



    [3] The system has infinite soluions.

    Example: . \begin{array}{ccc}x + y &=& 4 \\ 2x + 2y &=&8\end{array}


    If we try to solve the system, we get a true statement, like: . 0 = 0
    . . This indicates that the system has infinitely many solutions.


    The problem says: find two numbers whose sum is 4
    . . and if we double the numbers and add them, we get 8.

    We see that (3,1) is a solution . . . but so is (4,0),\;(5,-1),\;\hdots


    If we graph the lines, we get the same line twice.
    . . So, of course, they "intersect" each other a zillion times.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2009
    From
    Zagreb
    Posts
    65
    examples ( 2 variables ) :

    1. case

    x + y = 2

    x - y = 1

    this system has only one solution x = 3/2 , y = 1/2 ( 3/2, 1/2 )

    2. case

    x + y = 2

    2x + 2y = 4

    this system has infinite set of solutions

    ( x = t => y = 2 - t ) => solution is ( t , 2 - t ) = t*( 1, -1 ) + ( 0, 2 )

    where t is element of F ( F = R or C )

    3. case

    x + y = 2

    x + y = 4

    this system obvious has no solutions
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. System of equations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 22nd 2010, 06:07 AM
  2. need help with system of equations
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 21st 2010, 06:00 PM
  3. Replies: 2
    Last Post: April 20th 2010, 03:26 PM
  4. system of equations
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 1st 2009, 11:27 PM
  5. system of equations alg II
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 3rd 2008, 01:58 PM

Search Tags


/mathhelpforum @mathhelpforum