**Problem Analysis**
We are given that the breadth of a rectangle is 4 units less than its length. Let's assume the length of the rectangle to be 'k' units and the breadth to be 'b' units. We are also given that the perimeter of the rectangle is 20 units.

**Perimeter of a Rectangle**
The perimeter of a rectangle is the sum of all its sides. For a rectangle, the sum of the lengths of opposite sides is equal. Therefore, the perimeter of a rectangle can be calculated using the formula:

Perimeter = 2 * (Length + Breadth)

**Forming Linear Equations**
To model the given situation using a pair of linear equations, we can start by using the given information to write equations for the length and breadth of the rectangle.

1. Equation for the length:
Given that the breadth of the rectangle is 4 units less than its length, we can write the equation:
b = k - 4

2. Equation for the perimeter:
Given that the perimeter of the rectangle is 20 units, we can use the formula for the perimeter of a rectangle to write the equation:
2 * (k + b) = 20

**Simplifying the Equations**
Let's simplify the two equations to make them easier to work with.

1. Equation for the length:
We have b = k - 4. Rearranging this equation, we get:
k = b + 4

2. Equation for the perimeter:
Expanding the equation 2 * (k + b) = 20, we get:
2k + 2b = 20

**Final Pair of Linear Equations**
After simplifying the equations, we have the following pair of linear equations to model the given situation:

k = b + 4
2k + 2b = 20

These equations represent the relationship between the length and breadth of the rectangle, and the perimeter of the rectangle, respectively.

By solving these equations, we can find the values of 'k' and 'b' that satisfy both equations and represent the length and breadth of the rectangle.