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:

HelloClass, and happy final week! Since I had my daughter I like to shop morefor her than myself and I have determined a shopping situation suitablefor a linear equation.

A store has a sale on baby clothes. I can buy tops for $2.00 perpiece 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 waspretty straight-forward, elimination calls for multiplying and having tofigure factors in order to determine equal x-coefficients, which meansextra work.

Thank You

Jasmine

References:

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

POST2:

Hello class,

I sell two colors of the same product on Amazon, but they don’t giveme exact sales data until a couple days later. So, I have found thissystem 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 easierto convey and follow in writing. They’re both good ways of solving, butfor this assignment I’ve found the synthesis to be more preferable.

Cheers,

– Sam