Solving Linear Equations and Applications

This video tutorial covers linear equations and systems of equations. It introduces key vocabulary and concepts, such as constant terms and systems of equations. The video uses a balance hanger metaphor to explain solving linear equations and discusses equations with variables on both sides. It also explores systems of equations, using a real-world example of two cars traveling at different speeds to illustrate how to find when their distances are equal. The tutorial emphasizes understanding solutions graphically and algebraically.

What type of solutions can a linear equation have?

• No solution, one solution, or infinitely many solutions

• Only one solution

• No solution or one solution

• Only infinitely many solutions

Which of the following is a vocabulary term introduced in this unit?

• Quadratic term

• Logarithmic term

• Constant term

• Exponential term

What metaphor is used to explain solving linear equations?

• A seesaw

• A scale

• A balance hanger

• A pendulum

What happens when you add or subtract the same amount from both sides of an equation?

• The equation becomes unbalanced

• The equation becomes invalid

• The equation remains balanced

• The equation becomes more complex

In the balance hanger metaphor, what does the hanger represent?

• The variable

• The equation

• The solution

• The constant term

What is a system of equations?

• A quadratic equation

• A set of two or more equations with the same variables

• A single equation with multiple variables

• An equation with no solution

In the car example, what is the speed of Car A?

• 65 miles per hour

• 75 miles per hour

• 55 miles per hour

• 85 miles per hour

What is the equation for the distance of Car A from the rest area?

• d = 75T

• d = 55T

• d = 65T

• d = 85T

What is the equation for the distance of Car B from the rest area?

• D = 14 - 85T

• D = 14 - 65T

• D = 14 - 75T

• D = 14 - 55T

At what time are both cars equidistant from the rest area?

• 0.2 hours

• 0.1 hours

• 0.3 hours

• 0.4 hours