Solving Equations and Back Substitution

The video tutorial explains how to solve a system of three equations with three unknowns using back substitution. It begins by solving the third equation for Z, then substitutes Z into the second equation to solve for Y, and finally substitutes both Y and Z into the first equation to solve for X. The solution is presented as an ordered triple, demonstrating the methodical approach to solving such systems.

What is the first step in solving a system of equations using back substitution?

• Solve the first equation for X

• Solve all equations simultaneously

• Solve the second equation for Y

• Solve the third equation for Z

When solving for Z in the equation 2Z = -4, what is the value of Z?

• 4

• -2

• -4

• 2

After finding Z, what is the next step in back substitution?

• Substitute Z into the second equation

• Substitute Z into the first equation

• Solve for X directly

• Solve for Y directly

What is the value of Y when substituting Z = -2 into the equation 3Y - 2Z = -5?

• -5

• 5

• -3

• 3

What is the equation used to solve for X after substituting Y and Z?

• X + Y + Z = 0

• 3X + 2Y - Z = 0

• 2X - 4Y + 5Z = 0

• 4X - 3Y + 2Z = 0

What is the value of X after solving the equation 2X - 4(-3) + 5(-2) = 0?

• 1

• -1

• 2

• -2

What is the ordered triple solution for the system of equations?

• (1, 3, 2)

• (-2, 1, -3)

• (2, -1, 3)

• (-1, -3, -2)

In what order are the variables presented in an ordered triple?

• Y, Z, X

• Z, Y, X

• X, Y, Z

• Z, X, Y

What operation is used to isolate a variable when solving an equation?

• Multiplication

• Subtraction

• Division

• Addition

What is the purpose of back substitution in solving equations?

• To solve equations in reverse order

• To solve equations simultaneously

• To simplify equations

• To eliminate variables