Linear Systems of Equations in Two Variables

Date: 06/18/99 at 18:52:12
From: Jen
Subject: Word problem solving linear system of equations

The following is a problem from my math book. The chapter deals with 
linear systems of equations in two variables. I have tried for several 
hours to solve this problem to no avail. The graph is pretty close to 
what it looks like in the book. Please help. Thanks.


In the figure, parallelogram ABCD has a perimeter of 50 meters, and 
trapezoid AECD has a perimeter of 39 meters. Triangle EBC is isosceles 
with EB and BC having equal measure. Furthermore, AE and EC are equal 
in measure. Find the lengths of AE, EB and DC.

     A___________________E______B
      \                   \     \
       \                    \    \
        \                     \   \
         \                      \  \
          \                       \ \
           \                        \\
          D \________________________\\C

Date: 06/19/99 at 08:16:19
From: Doctor Jerry
Subject: Re: Word problem solving linear system of equations

Hi Jen,

Thanks for your question.

Let x = AD and y = DC. Then 

     AE =y-EB = y-BC = y-x.

Also,

     2x + 2y = 50 and

          AE  +   EC  + CD + DA = 39 
   or   (y-x) + (y-x) +  y +  x = 39.

That should do it.

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/