Question

Real-World Systems of Equations Discussion

Begin the discussion by responding to the following prompt:

Systems of linear equations can be used to solve many, but not all, real-world problems. When you chose the problem for your journal entry, how did you know that this problem could be solved using a system of linear equations? What specific characteristics does your problem have that made it a good choice? List at least three reasons why the problem you described in your journal prompt can be solved using a system of linear equations.

Post a detailed response to the questions about your choice of a real-world problem to solve using a system of linear equations. Then respond to two classmates’ posts.

Participate in the discussion to learn more about how to determine if a real-world problem can be solved using systems of linear equations.

Answer 1

[AI-generated answer — Bot GPT 3.5]

I chose a problem related to budgeting for a trip, where I needed to calculate how much money I could spend each day based on a total budget and number of days. I knew that this problem could be solved using a system of linear equations because it involved multiple unknown variables (daily spending and total budget) that could be represented by linear equations.

Three specific characteristics of my problem that made it a good choice for using systems of linear equations are:

1. Known relationships between variables: In my problem, I knew the relationship between the total budget, daily spending, and number of days. This allowed me to set up equations representing these relationships and solve for the unknown variables using a system of linear equations.

2. Linearity of the problem: The problem of calculating daily spending based on a total budget and number of days is a linear relationship. This means that the variables are directly proportional to each other and can be represented by linear equations. This linearity made it suitable for using a system of linear equations.

3. Solvability of the problem: Since the problem involved a fixed total budget and number of days, it was possible to set up and solve a system of linear equations to determine the daily spending amount. The problem was well-defined and had a clear solution, making it a good candidate for using systems of linear equations.

Overall, the characteristics of known relationships between variables, linearity of the problem, and solvability made the problem of budgeting for a trip a suitable choice for using a system of linear equations.

I look forward to reading about my classmates' choices of real-world problems and how they determined if they could be solved using systems of linear equations.