Results 1 to 7 of 7

Thread: Simultaneous equations

  1. #1
    Junior Member
    Joined
    Dec 2009
    Posts
    61

    Simultaneous equations

    x+y=7, x^2 - y^2 = 21
    How do I do this?
    Last edited by Detanon; Dec 13th 2009 at 09:21 AM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by Detanon View Post
    x+7=7, xsquared - ysquared = 21
    How do I do this?
    Did you make a typo? I ask because I only see one equation with y in.

    As is stands $\displaystyle x =0$ and $\displaystyle y = \pm i\sqrt{21}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,184
    Thanks
    80
    Do you not "see" that x=0 ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Dec 2009
    Posts
    61
    woops sorry, I fixed it now.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by Detanon View Post
    woops sorry, I fixed it now.
    As that's better

    You can use the difference of two squares on the quadratic

    $\displaystyle (x+y)(x-y) = 7(x-y) = 21 \: \: $

    $\displaystyle \therefore \: \: x-y = 3 \: \: \rightarrow \: \: x = 3+y$

    Sub in x=3+y into the first equation

    (3+y)+y=7

    Solve that for y then use the first equation (in either form) to find x
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Dec 2009
    Posts
    61
    I dont get how you get (x+y)(x-y).
    Follow Math Help Forum on Facebook and Google+

  7. #7
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by Detanon View Post
    I dont get how you get (x+y)(x-y).
    It is the difference of two squares.
    Difference of two squares - Wikipedia, the free encyclopedia

    From the difference of two squares we see that $\displaystyle x^2-y^2=(x+y)(x-y)$

    If you expand the right hand side using FOIL the LHS is obtained: $\displaystyle (x+y)(x-y) = x^2-xy+xy-y^2$

    Since $\displaystyle -xy+xy=0$ we get $\displaystyle (x+y)(x-y)=x^2-y^2$

    ============================

    EDIT: If you prefer you can use the substitution method

    $\displaystyle x = 7-y$

    $\displaystyle (7-y)^2-y^2=21$

    and solve that linear equation (y^2 cancels) but I think using the difference of two squares is easier
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simultaneous Equations 4 variables, 4 equations
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Dec 7th 2011, 04:06 PM
  2. Simultaneous Equations
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Mar 10th 2011, 05:26 AM
  3. Replies: 3
    Last Post: Feb 27th 2009, 07:05 PM
  4. Simultaneous equations?
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: Jun 24th 2008, 06:32 AM
  5. Simultaneous equations?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Jun 20th 2008, 04:03 AM

Search Tags


/mathhelpforum @mathhelpforum