Solving Systems of Equations with Three Variables

The video tutorial covers solving systems of equations with three variables using the elimination method. It includes three examples: one with a unique solution, one with no solution, and one with infinite solutions. The tutorial provides step-by-step guidance on how to manipulate equations to eliminate variables and solve for the remaining ones. It also encourages students to practice with a problem at the end.

What is a system of equations?

• An equation with no variables

• A set of equations with different variables

• Two or more equations that share variables

• A single equation with multiple variables

What is the first step in the elimination method?

• Add the equations

• Multiply the equations

• Check if the numbers are multiples

• Subtract the equations

In Example 1, which variable is eliminated first?

• p

• q

• r

• None

What is the result of adding the first and second equations in Example 1?

• 8p + 2q = 10

• 4p - 4q = -4

• 3p - q = 5

• 12p - 2q = 6

What does it mean if the result of an equation is 0 = 2?

• There is one solution

• There are infinite solutions

• The solution is undefined

• There is no solution

In Example 2, what is the result of subtracting the first equation multiplied by 2 from the third equation?

• 0 = 0

• 4p + 4q = -6

• 0 = 2

• 2p - q = 1

What does it mean if the result of an equation is 0 = 0?

• The solution is undefined

• There is no solution

• There are infinite solutions

• There is one solution

In Example 3, what is the result of subtracting the first equation from the third equation multiplied by 2?

• 4p + 4q = -6

• 0 = 0

• 0 = 2

• 2p - 4q = 8

What is the final solution for p, q, and r in Example 1?

• (1, 2, 3)

• (0, 0, 0)

• (2, -1, 3)

• (1, 3, 1)

What should you do if you get an incorrect answer in the practice question?

• Try again tomorrow

• Give up

• Skip to the next question

• Ask for help