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.
Participate in the discussion to learn more about how to determine if a real-world problem can be solved using systems of linear equations.
When choosing a problem for my journal entry that could be solved using a system of linear equations, I looked for certain characteristics that indicated it was a good choice. Specifically, I looked for problems that involved multiple unknown variables, relationships between those variables that could be represented as linear equations, and a need to find a solution that satisfied all of those equations simultaneously.
In my chosen problem, I was trying to calculate the cost of buying different numbers of apples and oranges. This problem can be solved using a system of linear equations for several reasons:
1. Multiple unknown variables: In this problem, the unknown variables are the cost of an apple and the cost of an orange. By setting up two equations (one for the cost of buying a certain number of apples and one for the cost of buying a certain number of oranges), I can solve for both unknown variables simultaneously.
2. Linear relationships: The relationships between the variables (cost of buying apples, cost of buying oranges, total cost) can be represented as linear equations. This means that the relationships are straight lines when graphed, making them easy to work with algebraically.
3. Need to satisfy all equations simultaneously: In order to find the cost of buying a specific number of apples and oranges, I need to find a solution that satisfies both equations at the same time. This is a key characteristic of problems that can be solved using systems of linear equations.
Overall, the problem I described in my journal prompt was well-suited to be solved using a system of linear equations because it involved multiple unknown variables, linear relationships between those variables, and a need to find a solution that satisfied all equations simultaneously. By recognizing these characteristics, I was able to confidently use a system of linear equations to solve the problem and find the cost of buying apples and oranges.