Systems of Equations with Three Variables

The video tutorial introduces systems of equations, explaining that they consist of two or more equations. It describes how a solution to a system is an ordered pair that satisfies all equations. The tutorial then progresses to systems with three variables, where the solution is an ordered triple. An example is provided, and the video concludes with a note on future learning about more complex systems.

What is a system of equations?

• A single equation with one variable

• Two or more equations grouped together

• A mathematical expression without an equal sign

• An equation with no variables

Which of the following is an example of a system of equations?

• x + 2 = 5

• z = 7

• y = 3x + 2

• 2y = x + 1 and 3x = 4y - 1

What is the solution to a system of equations with two variables called?

• Ordered pair

• Ordered triple

• Single value

• Matrix

In a system of equations, what must be true for the solution?

• The x and y values are the same for all equations

• The equations have no solution

• The y-values are different

• The x-values are different

What is a system of equations with three variables called?

• Single equation

• Matrix

• Ordered triple

• Ordered pair

Which of the following represents a system of equations with three variables?

• x + y = 2

• 2x + y - z = 5, x + y + z = -3, -2 - y + 2x = 2

• z = 7

• y = 3x + 2

What is the solution to a system of equations with three variables called?

• Single value

• Ordered triple

• Matrix

• Ordered pair

In the example given, what is the ordered triple solution to the system of equations?

• (0, 0, 0)

• (3, 2, 1)

• (2, 0, -1)

• (1, 1, 1)

What is the value of x in the ordered triple solution (2, 0, -1)?

• 0

• 1

• -1

• 2

What is the value of y in the ordered triple solution (2, 0, -1)?

• 0

• 1

• 2

• -1