Solving Systems Using Substitution

Question

Don has a rectangular lot that has a length five times greater than the width. The perimeter of the lot is 120 feet. Write a system of equations that can be used to find the length and width of the lot.

Answer 1

1. L = 5W

2. 120 = 2L + 2(5W)

3. 120 = 2(5W) + 2(5W)

4. 120 = 20W

5. 120/20 = W

6. 6 = W

7. L = 5(6)

8. L = 30 

 

W = 6 ft and L = 30 ft

Answer 2

The perimeter of a rectangle is the sum of twice of the width and twice the length.  A system of equation is when we have at least two equations with at least two different variables. 

 

Let width = x

Let length = y = 5x

Perimeter = 120

 

Using these variables, you can create an equation that represents the perimeter, and an equation that represents the length in terms of the width.

 

First equation:

 

2x + 2y = 120              

 

 

Second equation:

 

5x = y

 

Subtract y on both sides of the equation.

 

5x - y = 0                        

 

 

These are your two equations.

 

2x + 2y = 120                    eq1

5x - y = 0                           eq2