Question

Help? Linear equations using elimination?
The perimeter of a rectangle is 48 cm. The length is 6 cm less than twice the width. Which system would model this situation, and what are the length and the width?
A.
2l + 2w = 48
l + 2w = 6
Solution: (9, 6)
B.
2l + 2w = 48
2l + w = –6
Solution: (–32, 56)
C.
l + w = 48
l – 2w = –6
Solution: (18, 6)
D.
2l + 2w = 48
l – 2w = –6
Solution: (14, 10)

Answer 1

First you have to understand the problem. What formula do you need in order to model the problem?

Answer 2

The perimeter of a rectangle which is: \(P=2l+2w\)

Answer 3

Then write down all the given:
\(\Large {P=48 cm,\\ l=2w-6} \)

Answer 4

After these steps, substitute all the given into the formula

Answer 5

Tell me what you got and i'll check it later :)

Answer 6

I still don't understand... :(

Answer 7

which part you don't understand? O.o

Answer 8

I understand it, I just don't know where to substitute and what to substitute in.... Because I have to use elimination first..

Answer 9

you can do it later after you find all the equation you need. After that, you can use elimination to find the solutions.
so let's do substitution to find the first equation :)

since P=2l+2w and P=48, you will have \(2l+2w=48\)

Answer 10

did you get it?

Answer 11

Okay? There are two variables and you can't necessarily solve an equation once you've used substitution. I'm just so lost.

Answer 12

You just have to substitute the given into the formula for the perimeter of the rectangle to get an \(equation\). Think about this, how can you apply elimination if you don't have equations?

so you already have : 2l +2w = 48 as your first equation

From the given, you can find the second equation which is \(l=2w−6\)
you can rearrange this equation so that they will have the same format as the first equation: \(l-2w=6\)

Answer 13

i made a mistake, it should be: \(\LARGE l−2w=-6\), i forgot the negative.

Answer 14

did you understand already? I just used substitutions to get equations then you can apply elimination later once you have the equations :)

Answer 15

I'll try and solve it. Thank you.

Answer 16

no problem :)

Answer 17

Wait, so how am I supposed to use elimination when I can't solve this equation using elimination.
\[21+2w=48\]
\[l-2w=-6\]

Answer 18

For example, if I had
3y-4x=9
and
-3y+8x=-2
I could easily use elimination because both equations have a y and x variable.

Answer 19

you can. just add the two equations and the variable w will be eliminated then solve for l.

Answer 20

it's the same thing. instead of x and y, you are using l and w in this problem.

Answer 21

Okayyy I seeeee Thank youuu :D

Answer 22

Is the solution (14,10)?

Answer 23

great job! :) it's right

Answer 24

Thank you for helping me.

Answer 25

you're welcome as long as you understand it there will be no problem ;)

goodluck!