System of linear equations can be used to solve many, but not all real world problems when you choose the problem for your journal entry 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, include a few numbers for the linear equation. Explain in 2-4 sentences

Answer 1

I chose the problem of budgeting for a vacation as my journal prompt, and yes, I knew that this problem could be solved using a system of linear equations. This problem is a good choice for using linear equations because it involves multiple variables (expenses such as airfare, accommodations, activities, etc.) that can be represented as linear relationships. Additionally, the problem involves constraints such as the total budget amount and the total fixed expenses, making it suitable for a system of linear equations approach.

For example, let's say the total budget for the vacation is $3000. If the cost of airfare is represented as $800, accommodations as $1200, and activities as $400, the linear equation can be:
800x + 1200y + 400z = 3000

The problem can also involve inequalities, such as ensuring that the total expenses do not exceed the budget amount, which can be represented as:
800x + 1200y + 400z ≤ 3000