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### 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

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,

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/
```
Associated Topics:
High School Basic Algebra
High School Geometry
High School Triangles and Other Polygons
Middle School Algebra
Middle School Geometry
Middle School Triangles and Other Polygons

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