# mth122 peer discussion responses 150 words each

Please reply to both** POST1:** and **POST2**: I have also included the initial post Initial Post as reference. 150 words each

For this discussion, complete the following tasks:

- Write two linear equations with two variables that model something from your daily life.
- Solve the system of equations in two ways.
- Discuss which method you liked better and why.
- In your responses to peers, contrast your preferences for how to solve systems of equations.

**POST1:**

Hello Class, and happy final week! Since I had my daughter I like to shop more for her than myself and I have determined a shopping situation suitable for a linear equation.

A store has a sale on baby clothes. I can buy tops for $2.00 per piece and bottoms for $3.00 per piece. I bought a total of 13 pieces for $31.00 (What a deal!).

If tops=x and bottoms=y, my equations will be

(1) x+y=13

(2) 2x+3y=31

**Substitution Method:**

x+y=13

x=13-y

2(13-y)+3y=31

26-2y+3y=31

26+y=31

y=31-26

y=5

x+5=13

x=13-5

x=8

So x=8 and y=5 so 2(8)+3(5)=31 or 16+15=31

**Elimination Method:**

2x+3y=31 Multiply by 1 2x+3y=31

– x + y=13 Multiply by 2 – __2x+2y=26__

y=5

Then back-substitute 2x+3(5)=31

2x+15=31

2x=31-15

Divide both sides by 2

$\frac{2x=16}{2}$

x=8

So, again x=8 and y=5

I found substitution to be the easier method for me because it was pretty straight-forward, elimination calls for multiplying and having to figure factors in order to determine equal x-coefficients, which means extra work.

Thank You

Jasmine

References:

Bittinger, M. L., Beecher, J. A., Ellengoben, D. J., and Penna, J. (2016). *Algebra & trigonometry: Graphs and models *(6th ed.). [E-reader version]. Upper Saddle River, NJ: Pearson. Retrieved from http://www.pearsonmylabandmastering.com/northameri…

**POST2:**

Hello class,

I sell two colors of the same product on Amazon, but they don’t give me exact sales data until a couple days later. So, I have found this system of equations thing to be quite useful.

For instance: today I have sold 32 units for $574. I charge $20 for whites and $17 for blacks.

w+b=32

20w+17b=574

isolate b=32-w

20w+17(32-w)=574

20w+544-17w=574

20w-17w=30

3w=30

w=10

then plug into w+b=32 to find the amount of blacks I have sold today is 22

in interval form would be: (10,22)

to solve by elimination:

20w+17b=574

(w+b=32)-20

——————–

20w+17b=574

-20w-20b=-640

——————–

combine like terms

(-3b=-66)/-3

b=22

w+(22)=32

w=10 — or (10,22)

Personally, I like the synthesis method because its a little easier to convey and follow in writing. They’re both good ways of solving, but for this assignment I’ve found the synthesis to be more preferable.

Cheers,

– Sam