Results 1 to 3 of 3

Math Help - Setting up a system of equations! + Matrix solving

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    16

    Setting up a system of equations! + Matrix solving

    In a recent football game, KU scored 32 points in 9 scoring plays (from touchdowns worth 6 points each, extra points worth 1 point each, and field goals worth 3 points each), and got one more touchdown than extra point. Set up a system of equations to determine how many touchdowns, extra points, and field goals they made, then put this system into a matrix and s solve using row operations.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,861
    Thanks
    742
    Hello, ryno16!

    In a recent football game, KU scored 32 points in 9 scoring plays
    (Touchdowns = 6 points, extra points = 1 point, field goals = 3 points.)
    And got one more touchdown than extra points.

    Set up a system of equations to determine how many TDs, EPs, and FGs they made,
    then put this system into a matrix and solve using row operations.

    Let: . \begin{Bmatrix}T &=& \text{touchdowns} \\ E &=& \text{extra points} \\ F &=& \text{field goals} \end{Bmatrix}

    "32 points in 9 plays": . \begin{array}{ccc}T + E + F &=& 9 \\ 6T + E + 3F &=& 32 \end{array}

    "One more T than E": . T \:=\:E+1 \quad\Rightarrow\quad T - E \:=\:1


    We have: . \left|\begin{array}{ccc|c}<br />
1&1&1&9 \\ 6&1&3&32 \\ 1&\text{-}1&0 & 1 \end{array}\right|


    \begin{array}{c} \\ R_2-6R_1 \\ R_3-R_1\end{array}\left|\begin{array}{ccc|c} 1&1&1&9 \\ 0&\text{-}5& \text{-}3& \text{-}22 \\ 0& \text{-}2& \text{-}1 & \text{-}8 \end{array}\right|


    . . \begin{array}{c}\\ \text{-}1\cdot R_2 \\ \text{-}1\cdot R_3 \end{array} \left|\begin{array}{ccc|c}<br />
1&1&1&9 \\ 0&5&3&22\\ 0&2&1&8 \end{array}\right|


    \begin{array}{c}\\ R_2 - 2R_3 \\ \\ \end{array} \left|\begin{array}{ccc|c} 1&1&1&9 \\ 0&1&1&6 \\ 0&2&1&8 \end{array}\right|


    \begin{array}{c}R_1-R_2 \\ \\ R_3-2R_2 \end{array} \left|\begin{array}{ccc|c} 1&0&0&3 \\ 0&1&1&6 \\ 0&0&\text{-}1 & \text{-}4 \end{array}\right|


    . . \begin{array}{c} \\ \\ \text{-}1\cdot R_3\end{array} \left|\begin{array}{ccc|c} 1&0&0&3 \\ 0&1&1&6 \\ 0&0&1&4 \end{array}\right|


    \begin{array}{c}\\ R_2-R_3 \\ \\ \end{array} \left|\begin{array}{ccc|c} 1&0&0&3 \\ 0&1&0&2 \\ 0&0&1&4 \end{array}\right|


    Therefore: . \begin{Bmatrix}\text{3 touchdowns} \\ \text{2 extra points} \\ \text{4 field goals} \end{Bmatrix}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    16
    thank you so much! this helped an extreme amount!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Setting up system of differential equations, circuits.
    Posted in the Differential Equations Forum
    Replies: 14
    Last Post: October 1st 2010, 07:01 AM
  2. Setting up a system of equations for a matrix
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 29th 2010, 04:06 AM
  3. setting up a system of equations
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 31st 2009, 04:09 PM
  4. Matrix Inverse solving system of equations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 15th 2009, 05:48 AM
  5. Replies: 2
    Last Post: February 19th 2009, 11:48 PM

Search Tags


/mathhelpforum @mathhelpforum