Writing a System of Equations from a Context

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

How do you represent a cost equation for a service with a fixed fee and a variable fee?

Back

The cost can be represented as y = mx + b, where m is the variable cost per unit, x is the number of units, and b is the fixed fee.

Front

What does the slope represent in a cost equation?

Back

The slope represents the rate of change of cost with respect to the number of units. It indicates how much the total cost increases for each additional unit.

Front

How do you determine when two companies charge the same amount?

Back

Set the cost equations of both companies equal to each other and solve for the variable.

Front

What is the significance of the y-intercept in a cost equation?

Back

The y-intercept represents the fixed cost or initial charge before any units are added.

Front

How can you compare costs from two different companies?

Back

By writing the cost equations for both companies and finding the point where they intersect, you can determine which company is cheaper for a given number of units.

Front

What is the formula for the total cost of renting a car with a daily rate and a deposit?

Back

Total Cost = Daily Rate * Number of Days + Deposit.

Front

How do you find the number of units at which one service becomes cheaper than another?

Back

Set the cost equations of both services equal to each other and solve for the number of units.

Front

What is the role of the constant term in a linear equation representing cost?

Back

The constant term represents the fixed costs that do not change with the number of units.

Front

How do you write an equation for a service that charges per mile?

Back

The equation can be written as y = mx + b, where m is the cost per mile, x is the number of miles, and b is the pickup fee.