Final answer:
Keywords such as 'total cost,' 'perimeter,' 'sum,' and 'difference' are crucial for setting up systems of equations in application problems. They indicate the relationships between variables and guide the formulation of equations necessary for finding solutions.
Step-by-step explanation:
When solving application problems and writing systems of equations, certain keywords can help indicate the relationships between variables and the type of equations you'll need to formulate. Examples of these keywords include total cost, when referring to the overall expense which might involve a fixed and variable component, perimeter, when dealing with the total distance around a shape, sum, which is a signal for the addition of numbers or quantities, and difference, indicating subtraction is necessary.
For instance, take a situation where the cost of a service includes a one-time charge and a rate that depends on the number of hours of service. In this case, the 'total cost to a customer' would be a keyword indicating you need to consider both the fixed charge and the hourly rate, leading you to an equation of the form y = mx + b, where 'm' stands for the rate per hour and 'b' represents the one-time charge.
Recognizing these keywords is instrumental in correctly translating a word problem into a mathematical model. It is the first step in solving problems ranging from basic algebra to more advanced linear algebra applications. By spotting these keywords, you can more accurately set up your systems of equations and find the solution to the application problem.