Algebra 41 - Using Systems of Equations Versus One Equation

The video tutorial discusses methods for solving systems of linear equations, including substitution and elimination methods. It explores various problems, such as finding dimensions of dog pens, solving motion problems with vehicles, and calculating prices of movie tickets and drinks. The tutorial demonstrates how to express unknowns in terms of a single variable or use systems of equations to solve problems. It highlights the flexibility of these methods and introduces the concept of solving systems with three variables.

What method can be used to solve a system of two linear equations in two variables?

• Graphical method

• Substitution method

• Trial and error

• Matrix method

In the dog pen problem, what does the variable W represent?

• The total area of the pen

• The width of the pen

• The length of the pen

• The perimeter of the pen

How is the speed of the car represented in the motion problem?

• S / 2

• S - 10

• S + 10

• 2S

What is the total distance between the car and the bus after 3 hours?

• 720 miles

• 540 miles

• 360 miles

• 180 miles

In the pricing problem, what does the variable T represent?

• The price of popcorn

• The price of a ticket

• The price of a drink

• The total cost

How many drinks were purchased by the second group in the pricing problem?

• Two drinks

• Five drinks

• Three drinks

• Four drinks

What is the price of a drink in the pricing problem?

• $7

• $5

• $6

• $8

What is the main challenge when solving problems with three unknowns?

• Visualizing in two-dimensional space

• Using a system of three equations

• Setting up a single equation

• Finding the right variables

What additional item is introduced in the problem with three unknowns?

• Candy

• Popcorn

• Chips

• Soda

What method is suggested for solving systems with three variables?

• Graphical method

• Substitution method

• Elimination method

• Matrix method