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Solving Linear System of Equations: Elimination

  1. Sep 2, 2012 #1
    1. The problem statement, all variables and given/known data

    A general system of linear equations is
    ax+by=e
    cx+dy=f

    where a,b,c,d,e,f are constant values.

    a)Use elimination to solve for x and y in terms of a,b,c,d,e,f.

    b)Are there any values that a,b,c,d,e,f cannot have?


    3. The attempt at a solution

    For part A, I got x=(e-f)/(a-c), assuming using subtraction for elimination, but in the answers it says x=(de-bf)/(ad-bc). Why are the coefficients of y there?

    For part B, I think ad=/=bc because then both equations would cancel out, and it is either the exact same equation or has the same slope but parallel and never intersecting.

    for example, 15x+9y & 5x+3y
     
    Last edited: Sep 2, 2012
  2. jcsd
  3. Sep 2, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You need to show your work---how you got the answer, not just the answer itself.

    RGV
     
  4. Sep 2, 2012 #3
    using elimination by subtraction, solving for x:
    ax+by=e
    cx+dy=f

    (ax+by)-(cx+dy)=(e-f)
    ax-cx +by-dy=(e-f)
    (a-c)x=(e-f)
    x=(e-f)/(a-c)

    Nevermind, I just realized that it's to make the coefficients of y the same.

    (ad)x+[STRIKE](bd)y[/STRIKE]=(de)
    (cb)x+[STRIKE](bd)y[/STRIKE]=(bf)
     
    Last edited: Sep 2, 2012
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