Results 1 to 3 of 3

Math Help - Solve for (x; y) in the system

  1. #1
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Solve for (x; y) in the system

    can anybody please Solve for (x; y) in the system?

    Solve for (x; y) in the system-pre-cal.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,653
    Thanks
    1478
    Equation 1 - Equation 2:

    \displaystyle [(e^x + 2)^2 - y] - [4(e^x + 2) - y] = 3 - (-1)

    \displaystyle (e^x + 2)^2 - 4(e^x + 2) = 4

    \displaystyle (e^x + 2)^2 - 4(e^x + 2) - 4 = 0.


    Now let \displaystyle X = e^x + 2 so that you get the quadratic

    \displaystyle X^2 - 4X - 4 = 0

    \displaystyle X^2 - 4X + (-2)^2 - (-2)^2 - 4 = 0

    \displaystyle (X-2)^2 - 8 = 0

    \displaystyle (X-2)^2 = 8

    \displaystyle X-2 = \pm 2\sqrt{2}

    \displaystyle X = 2\pm 2\sqrt{2}

    \displaystyle e^x + 2 = 2\pm 2\sqrt{2}

    \displaystyle e^x = \pm 2\sqrt{2}.


    Since \displaystyle e^x > 0 for all \displaystyle x

    \displaystyle e^x = 2\sqrt{2}

    \displaystyle x = \ln{(2\sqrt{2})}

    \displaystyle x = \ln{(2^{\frac{3}{2}})}

    \displaystyle x = \frac{3}{2}\ln{2}.


    Now back-substitute to find \displaystyle y.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2
    amazing! the best!
    y = 9 + 8 sq rt. 2

    thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. solve system
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 3rd 2011, 03:53 PM
  2. Solve the system
    Posted in the Algebra Forum
    Replies: 0
    Last Post: January 31st 2010, 08:57 AM
  3. Can't solve system
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 20th 2010, 12:10 PM
  4. solve the system
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 2nd 2007, 08:19 PM
  5. Solve System of Dif EQ
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 31st 2007, 07:42 AM

Search Tags


/mathhelpforum @mathhelpforum