Solving Systems of Equations by Substitution

Professor Von Schmohawk introduces a lecture on finding the intersection point of two graphs, using the tortoise and hare race as an example. The lecture focuses on the substitution method to solve a system of equations, demonstrating how to find the exact time and distance when the tortoise and hare meet. The process involves substituting one equation into another to solve for variables, verifying the solution, and converting results into mixed numbers. The lecture concludes with a preview of the elimination method for solving equations.

What was the hare doing during the first four hours of the race?

• Sleeping

• Reading an Algebra book

• Running at full speed

• Waiting at the starting point

At what time did the hare overtake the tortoise?

• Between 5 and 6 hours

• Exactly at 4 hours

• Before 5 hours

• After 6 hours

What was the purpose of graphing the distances of the tortoise and hare?

• To determine who won the race

• To identify the point where they meet

• To illustrate their starting points

• To find the speed of each racer

Which mathematical method is demonstrated to find the intersection point?

• Elimination

• Integration

• Graphing

• Substitution

What does the value of 'y' equal according to the second equation?

• The square of x

• x minus 2

• Two times x

• One-half of x

What is the final value of x found through substitution?

• Twelve-thirds

• Four-thirds

• Eight-thirds

• Sixteen-thirds

How is the value of y determined after finding x?

• By adding x to sixteen-thirds

• By setting x in the first equation

• By multiplying x with two

• By setting x in the simplest equation

What does the intersection point represent in terms of time and distance?

• Five hours, two miles

• Four hours, two miles

• Six hours, three miles

• Five hours and twenty minutes, two and two-thirds miles

Why is the method used in the example called 'substitution'?

• Because it involves substituting values from one equation into another

• Because it uses graphical methods to solve

• Because it eliminates one variable at a time

• Because it requires the multiplication of both equations

What is the next method of solving systems of equations to be introduced?

• Division

• Elimination

• Substitution

• Graphical