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.
I chose the problem of determining the cost of purchasing tickets for a concert because I knew this problem could be solved using a system of linear equations due to the following characteristics:
1. Linear relationship: The relationship between the number of tickets purchased and the total cost is linear. Each additional ticket purchased incurs the same cost, leading to a linear relationship between the number of tickets and the total cost.
2. Proportional increase: The total cost increases in a proportional manner with the number of tickets purchased. This indicates that the problem can be modeled using a linear equation, where the coefficient represents the cost per ticket.
3. Consistent pricing: The problem involves a consistent price per ticket, indicating that the relationship between the number of tickets purchased and the total cost is linear. This allows us to set up a system of linear equations to solve for the cost per ticket and the total cost for a given number of tickets.