Algebra 35 - Systems of Linear Equations in Two Variables

Professor Von introduces geometric relationships in linear equations using a race between a tortoise and a hare. The video explains how to graph the distance of each animal over time, derive equations for their paths, and find the intersection point where they meet. The concept of using mathematical techniques to determine the coordinates of intersection is highlighted, setting the stage for the next lecture on substitution.

What is the significance of the intersection points when graphing two linear equations?

• They indicate the common solutions to both equations.

• They show where the two lines are parallel.

• They represent the average of the two equations.

• They highlight the maximum distance between the lines.

In the race between the tortoise and the hare, what was the initial speed of the tortoise?

• 1 mile per hour

• 1/2 mile per hour

• 2 miles per hour

• 3 miles per hour

How long did the hare wait before starting the race?

• 3 hours

• 2 hours

• 5 hours

• 4 hours

What is the equation for the tortoise's distance as a function of time?

• y = x

• y = 1/2 x

• y = 2x

• y = x - 2

Which form is used to derive the equation for the hare's distance?

• Slope-intercept form

• Quadratic form

• Point-slope form

• Exponential form

What is the slope of the hare's graph?

• 3

• 1

• 1/2

• 2

What technique will be introduced in the next lecture to find the intersection point of the graphs?

• Elimination

• Substitution

• Graphical method

• Matrix method