Solving Systems of Equations and Linear Models

The video tutorial covers CSD Math 8 Unit 5 Lesson 9 on linear models. It begins with an example of a small company selling a board game and explores whether the sales data can be modeled linearly. The tutorial includes graphing the sales data, estimating future sales, and solving a water tank problem using linear functions. It concludes with a step-by-step solution to a system of equations.

What is the main purpose of using a linear model in the board game sales example?

• To compare sales with another company

• To determine the exact number of games sold each month

• To estimate future sales based on past data

• To find the maximum sales in a given month

When plotting the sales data on a graph, what are you primarily looking for?

• A linear trend

• A perfect curve

• Random points

• A circular pattern

If the sales data forms a linear model, what can it help you predict?

• The total revenue generated

• The best-selling game

• The trend of sales over time

• The exact number of games sold each day

In the water tank example, what is the independent variable?

• The amount of water

• The rate of water flow

• The number of hours

• The size of the tank

What does the constant rate of 3 gallons per hour represent in the water tank example?

• The amount of water added each hour

• The total water capacity

• The time taken to fill the tank

• The speed of water flow

How do you determine the amount of water in the tank after a certain number of hours?

• By dividing the hours by the rate

• By adding the hours to the rate

• By subtracting the rate from the hours

• By multiplying the hours by the rate

What is the first step in solving the system of equations presented?

• Adding the equations together

• Substituting one equation into the other

• Graphing the equations

• Multiplying both equations by a constant

In the system of equations, what does the negative sign in front of a term indicate?

• The term is incorrect

• The term should be ignored

• The term is subtracted

• The term is added

What is the solution to the system of equations in terms of x?

• x = -8

• x = 8

• x = -7

• x = 7

After finding x, how do you determine the value of y in the system of equations?

• By dividing x by the equation

• By substituting x back into one of the original equations

• By ignoring x and solving for y directly

• By adding x to the equation