Results 1 to 12 of 12

Math Help - Solving Linear Systems by Elimination

  1. #1
    Junior Member
    Joined
    Oct 2008
    From
    Scarborough
    Posts
    44

    Solving Linear Systems by Elimination

    Edit: Sorry, just noticed it's in the wrong Categorie.

    Hello, I did all this last year, but didn't memorize it Now when I look back, I dont know what to do ... I would be greatful If anyone could answer the following questions. Seeing the solution might help me understand the other questions.


    1. Solve the following linear systems of equations using substitution.
      1. y = 3x + 5
        y = 2x + 4
      2. 2x + y = 7
        4x - y = 23

    2. Solve the following linear systems using elimination. Check your solutions.
      1. 3x - 2y = 18
        x + y = 16
      2. 5x + 2y = 10
        3x - 4y = -46

    3. A barnyard has cows and chickens. There are 34 heads and 86 legs. If w represents the number of cows and k represents the number of chickens:
      1. Write a linear system of equations to model this situation.
      2. Solve the linear system to find the number of cows and the number of chickens in the barnyard.
      3. Verify your solution by providing a graphical solution. You can use a spreadsheet or Geometer's Sketchpad.


    Sincerely,

    Serialkisser
    Last edited by Serialkisser; October 23rd 2008 at 12:04 PM. Reason: Mistake
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Aug 2008
    Posts
    530

    Reply

    Quote Originally Posted by Serialkisser View Post
    Edit: Sorry, just noticed it's in the wrong Categorie.

    Hello, I did all this last year, but didn't memorize it Now when I look back, I dont know what to do ... I would be greatful If anyone could answer the following questions. Seeing the solution might help me understand the other questions.


    1. Solve the following linear systems of equations using substitution.
      1. y = 3x + 5
        y = 2x + 4
    Put the value of y from first equation to second

    3x + 5 = 2x + 4

    x = -1

    y = 2

    solve next question in the same way.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Aug 2008
    Posts
    530
    Quote Originally Posted by Serialkisser View Post
    Edit: Sorry, just noticed it's in the wrong Categorie.

    Hello, I did all this last year, but didn't memorize it Now when I look back, I dont know what to do ... I would be greatful If anyone could answer the following questions. Seeing the solution might help me understand the other questions.


    1. Solve the following linear systems using elimination. Check your solutions.
      1. 3x - 2y = 18
        ( x + y = 16 ) . 2
    Multiply second equation by 2 and add to first equation,

    3x - 2y = 18
    2x + 2y = 32
    ---------------------------
    5x = 50
    ---------------------------
    x = 10
    so, y = 6

    do next Ques in the same way.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Aug 2008
    Posts
    530
    Quote Originally Posted by Serialkisser View Post
    Edit: Sorry, just noticed it's in the wrong Categorie.

    Hello, I did all this last year, but didn't memorize it Now when I look back, I dont know what to do ... I would be greatful If anyone could answer the following questions. Seeing the solution might help me understand the other questions.

    1. A barnyard has cows and chickens. There are 34 heads and 86 legs. If w represents the number of cows and k represents the number of chickens:
      1. Write a linear system of equations to model this situation.
      2. Solve the linear system to find the number of cows and the number of chickens in the barnyard.
      3. Verify your solution by providing a graphical solution. You can use a spreadsheet or Geometer's Sketchpad.


    Sincerely,

    Serialkisser
    Since there are 34 heads,

    w + k = 34 .....................(1)

    since there are 86 legs,

    4w + 2k = 86 ..................(2)

    Now, solve these two equations by any of the method.

    See the attached graph for graphical solution (9, 25)
    Attached Thumbnails Attached Thumbnails Solving Linear Systems by Elimination-graph10.jpg  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Oct 2008
    From
    Scarborough
    Posts
    44
    How do I solve the word problem ?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Oct 2008
    From
    Scarborough
    Posts
    44
    Quote Originally Posted by Shyam View Post
    Put the value of y from first equation to second

    3x + 5 = 2x + 4

    x = -1

    y = 2

    solve next question in the same way.
    Hmmm I tried, but got a different solution for Y

    3x+5 = 2x+4

    3x-2x = 4-5

    -1x = 1
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Banned
    Joined
    Aug 2008
    Posts
    530
    Quote Originally Posted by Serialkisser View Post
    Hmmm I tried, but got a different solution for Y

    3x+5 = 2x+4

    3x-2x = 4-5

    -1x = 1
    so, you got

    x = -1

    Now, put this value of x in first equation

    y= 3x + 5

    y = 3(-1) +5

    y = -3 + 5
    y= 2

    Now, you got it ???
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Oct 2008
    From
    Scarborough
    Posts
    44
    I see, but the second part ( y=2x+4) wasn't used ... why ?

    U also wrote :

    Multiply second equation by 2 and add to first equation,

    3x - 2y = 18
    2x + 2y = 32
    ---------------------------
    5x = 50
    ---------------------------
    x = 10
    so, y = 6
    How do you know by what to multiply ?

    Sorry for all that, I take online Classes :-)
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Banned
    Joined
    Aug 2008
    Posts
    530
    Quote Originally Posted by Serialkisser View Post
    Edit: Sorry, just noticed it's in the wrong Categorie.

    Hello, I did all this last year, but didn't memorize it Now when I look back, I dont know what to do ... I would be greatful If anyone could answer the following questions. Seeing the solution might help me understand the other questions.


    1. Solve the following linear systems of equations using substitution.
      1. 2x + y = 7
        4x - y = 23
    from first EQN,

    y = 7 - 2x

    Put this value of y in second EQN,

    4x - (7 - 2x) = 23

    4x - 7 +2x = 23

    6x = 23 + 7

    x = 30/6 = 5

    so, y = 7 - 2x = 7 - 2(5) = -3
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Banned
    Joined
    Aug 2008
    Posts
    530
    Quote Originally Posted by Serialkisser View Post
    I see, but the second part ( y=2x+4) wasn't used ... why ?

    U also wrote :



    How do you know by what to multiply ?

    Sorry for all that, I take online Classes :-)
    I multiplied second eqn by 2 to make the coefficients of y equal in both eqns.

    go to the next page
    Last edited by Shyam; October 26th 2008 at 10:06 AM.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Banned
    Joined
    Aug 2008
    Posts
    530
    Quote Originally Posted by Serialkisser View Post
    Edit: Sorry, just noticed it's in the wrong Categorie.

    1. Solve the following linear systems using elimination. Check your solutions.
      1. 5x + 2y = 10
        3x - 4y = -46
    Now, you see, in first eqn, coefficient of y is +2
    and in second eqn, coefficient of y is -4
    so, if you multiply first eqn by 2, the coefficient of y will be +4, and it will get cancelled by -4 of second eqn, if we add these two eqns.

    so,

    10x + 4y = 20
    3x - 4y = -46
    ---------------------
    13x = -26 <--------------- by adding the two eqns, (+4y and -4y get cancelled)
    ---------------------

    x = -26/13 = -2

    For calculating y, put this value of x = -2 in any of the eqn,

    5(-2) + 2y = 10

    -10 + 2y = 10

    2y = 10 + 10

    y = 20/2 = 10

    Did you get it now???

    Now, can you solve the Question #3, (cows and chickens) the two eqns provided by me, by elimination method??? The graph already show you the answer.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Junior Member
    Joined
    Oct 2008
    From
    Scarborough
    Posts
    44
    Now I understand everything, thanks for your help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving Linear Systems by Elimination
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 26th 2011, 09:41 AM
  2. Solving Systems Using Elimination
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 3rd 2009, 03:52 AM
  3. Solving Systems Using Elimination
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 2nd 2009, 06:21 PM
  4. Replies: 7
    Last Post: September 19th 2008, 01:26 PM
  5. Replies: 3
    Last Post: October 11th 2006, 09:15 PM

Search Tags


/mathhelpforum @mathhelpforum