Question

The perimeter of a rectangle is 22 meters and the length is 7 meters longer than the width. Find the dimensions of the rectangle. Letx = the length and y = thewidthThe corresponding modeling system is:2x+2y=22x-y=7Use the method of substitution to solve this system

Answer 1

We have the following system of equations:

2x + 2y = 22

x - y = 7

The system can be solved in several ways, we are required to use the substitution method

First, we divide the first equation by 2:

x + y = 11

x - y = 7

Solve the first equation for x:

x = 11 - y

And substitute into the second equation:

(11 - y) - y = 7

Simplify:

11 - y - y = 7

11 - 2y = 7

Subtract 11:

-2y = 7 - 11 = -4

Divide by -2:

y = -4/(-2)

y = 2

Now replace this value to find x:

x = 11 - y = 11 - 2 = 9

Solution: x = 9, y = 2