Results 1 to 5 of 5

Math Help - Reasoning behind Solving using Substitution

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    16

    Reasoning behind Solving using Substitution

    Hello all, I'm brushing up my basic Math knowledge. Sometimes I have a hard time really understanding why things work the way they do. Now it's in the topic of Systems of Equations: Substitution method.

    Untill the graphing method it seemed all very clear to me. You have 2 lines (equations) and you are looking for the intersection point. Clear!

    Then comes the substitution method: I know how to use it. I can get to the right answers. But I just don't seem to see, get, or understand why this works.

    Example:
    4x + 3y = -8
    2x + y = 5

    Step 1: solve for one variable. So I make: y = 5 - 2x. Clear.
    Step 2: Fill in other equation: 4x + 3 (5 - 2x) = -8. I don't seem to really get it from this part...

    Can someone provide me with the simple breakthrough insight ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,707
    Thanks
    1470

    Re: Reasoning behind Solving using Substitution

    When you solve for y= 5- 2x, you are just saying that "y" and "5- 2x" are the same thing. Whatever you do to one, you can do to the other. The first equation says that if you multiply y by 3 and add 4x, you get -8. Since y is the same as 5-2x, if you multiply 5-2x by 3 and add 4x, you still get -8: 4x+ 3y= 4x+ 3(5- 2x)= 4x+ 15- 6x= 15- 2x= -8
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2011
    Posts
    16

    Re: Reasoning behind Solving using Substitution

    Thanks for the reply. I'm afraid I'm still not there.

    I don't seem to get why I can use the "Y" of ANOTHER equation for one equation. Maybe I still don't have a clear picture of the relationship between the two seperate equations..

    The only thing you are doing when 'solving' this system of equations is finding the intersection of the lines right?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901

    Re: Reasoning behind Solving using Substitution

    At the point of intersection, the y value will be the same for both equations. this is the fundamental concept.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,707
    Thanks
    1470

    Re: Reasoning behind Solving using Substitution

    The whole point of "simultaneous equations" is that you are seeking values of x and y that will satisfy both equations. The same y must satisfy both equations.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving Using Substitution
    Posted in the Algebra Forum
    Replies: 6
    Last Post: November 29th 2011, 01:35 PM
  2. solving for substitution
    Posted in the Algebra Forum
    Replies: 9
    Last Post: August 11th 2010, 04:12 AM
  3. Solving an integral using ash substitution
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 30th 2010, 08:09 PM
  4. Solving Integral using substitution
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 26th 2008, 02:11 PM
  5. Help solving and reasoning a word problem.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 3rd 2008, 09:01 PM

Search Tags


/mathhelpforum @mathhelpforum