Solving Systems of Equations

The video tutorial covers practice problem 3 from lesson 13, focusing on solving systems of equations. It explains how to find the intersection point of two lines by understanding the system of equations, using both graphical reasoning and algebraic methods. The tutorial demonstrates calculating differences in y-intercepts and slopes, and how these relate to finding the solution point where both equations intersect.

What is the main goal when solving a system of equations graphically?

• To determine the slope of each line

• To find the x-intercepts of both lines

• To find the intersection point of the lines

• To calculate the y-intercepts of the lines

How do you calculate the difference in y-intercepts between two equations?

• By subtracting the smaller y-intercept from the larger one

• By adding the y-intercepts of both equations

• By dividing the larger y-intercept by the smaller one

• By multiplying the y-intercepts of both equations

What does the difference in slopes tell us about the movement of the lines?

• It shows how fast the lines are moving away from each other

• It indicates the rate at which the lines are moving towards each other

• It determines the y-intercept of the lines

• It helps in finding the x-intercept of the lines

If two lines are 12 units apart on the y-axis and move towards each other at 6 units per x, how many x units will it take for them to intersect?

• 2 units

• 4 units

• 1 unit

• 3 units

What is the x-coordinate of the intersection point in this problem?

• 4

• 1

• 3

• 2

How can you find the y-coordinate once you have the x-coordinate of the intersection?

• By subtracting the x-coordinate from the y-intercept

• By adding the x-coordinate to the y-intercept

• By multiplying the x-coordinate with the slope

• By using the x-coordinate in either equation

What is the first step in solving the system algebraically?

• Calculating the difference in y-intercepts

• Determining the slope

• Finding the x-intercept

• Solving for y

What operation is used to eliminate the y-intercept in the algebraic solution?

• Addition

• Subtraction

• Multiplication

• Division

How do you determine the number of x units needed to close the gap between the lines?

• By dividing the difference in y-intercepts by the difference in slopes

• By subtracting the slopes of both lines

• By multiplying the difference in y-intercepts by the difference in slopes

• By adding the slopes of both lines

What is the final coordinate pair that represents the solution to the system of equations?

• (2, 5)

• (4, 7)

• (1, 4)

• (3, 6)