4B.3 Day 1 Solving System of Equations Word Problems

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

What does it mean to solve a system of equations word problem?

Back

It means to translate a real-world scenario into mathematical equations and find the values of the variables that satisfy all equations.

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 C = fixed fee + (variable rate × number of units).

Front

If Company A charges a fixed fee plus a variable rate, how do you find when it equals Company B's variable rate?

Back

Set the equations equal to each other and solve for the variable representing the number of units.

Front

What is the first step in solving a word problem involving two companies with different pricing structures?

Back

Identify the fixed and variable costs for each company and write equations based on the information given.

Front

How do you determine the cost per item from a total cost?

Back

Divide the total cost by the number of items purchased.

Front

What is the significance of finding the intersection point in a system of equations?

Back

The intersection point represents the solution where both equations are satisfied, indicating the values of the variables.

Front

How can you set up an equation from a word problem involving multiple items with different prices?

Back

Assign variables to each item, write an equation based on the total cost, and include the quantities of each item.

Front

What is a fixed fee in a pricing model?

Back

A fixed fee is a one-time charge that does not change regardless of the quantity of service or product used.

Front

What is a variable cost in a pricing model?

Back

A variable cost changes based on the quantity of service or product used, such as hourly rates or per-mile charges.