Solving Systems of Equations with Tables and Graphs

The video tutorial covers Chapter 3, focusing on solving systems of linear equations using tables and graphs. It begins with a review of systems of equations and introduces methods like graphing and using tables. Example 1 demonstrates solving a system graphically and with a table. Example 2 applies these methods to a real-life problem involving shark growth rates. Example 3 uses linear regression to predict when NYC and LA populations will be equal. The tutorial concludes with classifying systems as independent, dependent, or inconsistent.

What is a system of equations?

• A single linear equation

• A set of two or more equations

• A quadratic equation

• An equation with no variables

What form is used to represent linear equations in a system?

• Logarithmic form

• Quadratic form

• Exponential form

• Standard form or slope-intercept form

In Example 1, what is the point of intersection for the given system of equations?

• (0, 0)

• (-4, -2)

• (-2, -4)

• (4, 2)

What is the slope of the first equation in Example 1 after converting to slope-intercept form?

• 3/2

• 1/2

• -1/2

• 2/3

When using a table to solve a system of equations, what are you looking for in the table?

• When the slopes are equal

• When the y-values are equal

• When the x-values are equal

• When the intercepts are equal

In Example 2, what is the growth rate of the spiny dogfish shark?

• 0.75 cm per year

• 1.5 cm per year

• 1 cm per year

• 2 cm per year

At what age will the spiny dogfish and Greenland shark be the same length?

• 10 years

• 15 years

• 20 years

• 25 years

In Example 3, what year corresponds to the x-value of 87?

• 2037

• 1950

• 2000

• 2020

What is the predicted population of NYC and LA in the year 2037?

• 30.1 million

• 25.6 million

• 22.3 million

• 20.5 million

What type of system has no solution?

• Consistent system

• Dependent system

• Inconsistent system

• Independent system