The perimeter of a rectangle is 40cm. If the length were doubled and the width halved, the perimeter would be increased by 16cm. Find the dimensions of the original rectangle. Please use system of linear equations by elimination OR substitution. I need the work as well please.

The dimensions of the original rectangle are Length =12cm, Width=8cm

Step-by-step explanation

Let the length of the rectangle be x

Let the width of the rectangle be y

The perimeter of a rectangle is 40cm.

2(x+y)=40

Divide both sides by 2

x+y=20

If the length were doubled(2x) and the width halved(y/2), the perimeter would be increased by 16cm,i.e.(40+16)cm

Therefore:

Divide both sides by 2

From the first equation, x=20-y.

Substitute x=20-y into  

linear pair postulates