# 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:

1. Write two linear equations with two variables that model something from your daily life.
2. Solve the system of equations in two ways.
3. Discuss which method you liked better and why.
4. 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