Results 1 to 4 of 4

Math Help - system of liner equation

  1. #1
    Newbie
    Joined
    Dec 2010
    From
    Hong Kong
    Posts
    5

    system of liner equation

    Hello everyone. I have a question about system of liner equation.
    In wiki,I found an statement which is talking about it is possible for a system of two equations and two unknowns to have no solution (if the two lines are parallel), or for a system of three equations and two unknowns to be solvable (if the three lines intersect at a single point).
    I understand that the parallel lines have no common intersect point .So there exist no solution. However, I don’t understand the last one. This question defeats me for a long time. Can someone help me please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Quote Originally Posted by kenpoon View Post
    In wiki,I found an statement which is talking about it is possible for a system of two equations and two unknowns to have no solution (if the two lines are parallel), or for a system of three equations and two unknowns to be solvable (if the three lines intersect at a single point).
    I don't think you have finished explaining the gap in your understanding.

    I take two ideas here.

    A system of 3 eqns each with 2 unknowns have one (or maybe infinite) solution(s) if they intersect at the same point.

    A system of 3 eqns each with 2 unknowns have no solutions if they all share the same gradient but intersect the y-axis at different points.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2010
    From
    Hong Kong
    Posts
    5
    Thank you for your reply. I don't understand that the 3 eqns each with 2 unknowns have infinite solution(s) if they intersect at the same point.
    Why they have infinite solutions? They are just intersect at one point only.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,242
    Thanks
    1795
    Think about the three equations 2x+ 3y= 4, x- y= 5, 4x- 4y= 20 in the two unknowns, x and y. The last two equations are "dependent" (4x- 4y= 20 is just 4(x- y= 5) so they are not really "two" equations) so this really the same as two equations in two unknowns. That is the case where three equations in two unknowns have a single solution.

    Think about the three equations 2x+ 3y= 4, 6x+ 9y= 12, 8x+ 12y= 16 in the two unknowns, x and y. Those are all really the same equation (the second is 3 times the first and the third is 4 times the first) so any x and y that satisfy 2x+ 2y= 4 satisfy all three. Of course they do NOT "itersect at the same point". I believe pickslides misspoke there.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 2nd Order Liner PDE’s Part 1
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: March 26th 2011, 03:28 AM
  2. Systems of Liner Equations
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 14th 2010, 08:30 PM
  3. Two Liner Algebra Problems
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: August 17th 2009, 09:18 PM
  4. Liner equations and inequalities
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 17th 2008, 12:55 PM
  5. liner inequalities
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 11th 2006, 06:52 AM

Search Tags


/mathhelpforum @mathhelpforum