Question

the perimeter of your closet is equal to 18 feet. the differnece of the length and the width equals 1 foot. write a system of linear equations which represents the perimeter of your closet in respect to its width (x-axis) and length (y-axis)?

Answer 1

The equation is 2x+2y=18
y-x=1

Answer 2

The system of linear equations is

`\left \{ {{2x+2y=18} \atop {y-x=1}} \right.`

And the solution is
`(x,y)=(4,5)`

Explanation:

In order to make a system of linear equations which represents the perimeter of the closet in respect to its width ''x'' and length ''y'', we are going to read the exercise to make the equations.

''The perimeter of your closet is equal to 18 feet''

The perimeter is the sum of the outline from the closet.

The outline is formed with two widths and two lengths.

We can write the following equation :

`Perimeter=x+x+y+y=2x+2y`

Where the variable ''x'' represents the width and the variable ''y'' represents the length.

The perimeter is equal to 18 feet. Therefore we can write the first equation of our system of linear equations :

`2x+2y=18` (I)

We also know that ''The difference of the length and the width equal 1 foot''.

Therefore we can write :

`y-x=1` (II)

Our system of linear equations is formed with (I) and (II) :

`\left \{ {2x+2y=18} \atop {y-x=1}} \right.`

If we want to solve this system, from equation (II) we can write

`y-x=1`

`y=1+x` (III)

Replacing (III) in (I) :

`2x+2y=18`

`2x+2(1+x)=18`

`2x+2+2x=18`

`4x=16`

`x=4`

Replacing this value of ''x'' in (II) :

`y-x=1`

`y-4=1`

`y=5`

We find that
`x=4` and
`y=5` and the system of linear equations is :

`\left \{ {{2x+2y=18} \atop {y-x=1}} \right.`