Learn to solve a system of three equations

The video tutorial explains how to solve a system of three variables by eliminating one variable to reduce it to a system of two variables. The instructor demonstrates the elimination method and substitution method to find the values of x, y, and z. The process involves labeling equations, choosing a variable to eliminate, and solving the resulting equations to find the final solution.

What is the first step in solving a system of equations with three variables?

• Substituting variables

• Graphing the equations

• Labeling the equations

• Finding the determinant

Which variable is preferred to be eliminated first in a system of equations?

• A variable with a coefficient of 1

• A variable with a coefficient of 0

• A variable with a coefficient of 3

• A variable with a coefficient of 2

What operation is performed on equation 2 to eliminate y when using equations 1 and 2?

• Add 2

• Divide by 2

• Multiply by 2

• Multiply by -1

What is the result of eliminating y between equations 1 and 2?

• Equation A

• Equation C

• Equation B

• Equation D

What is the new equation formed after eliminating y between equations 2 and 3?

• 3x - z = 5

• 5x + 10z = 39

• 7x + 12z = 35

• x + y = 7

Which method does the instructor prefer for solving the reduced system of two variables?

• Graphing

• Substitution

• Matrix method

• Trial and error

What is the final solution for the system of equations?

• x = 5, y = 7, z = 0

• x = 7, y = 5, z = 0

• x = 5, y = 0, z = 7

• x = 0, y = 5, z = 7