Solving Systems of Equations with Three Variables

The video tutorial by Sandro Curió explains how to solve a system of equations with three variables using both the elimination and substitution methods. The instructor provides a detailed step-by-step guide, starting with the elimination of one variable to simplify the system into two equations. The tutorial then demonstrates solving the simplified system using substitution, ultimately finding the values of all variables. The video concludes with a summary of the solution process and emphasizes the importance of choosing the right method for different scenarios.

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

• Add all three equations together

• Eliminate one variable from two equations

• Multiply all equations by a constant

• Isolate one variable in each equation

Which variable should you choose to eliminate first?

• The variable that is easiest to eliminate

• The variable that appears in all equations

• The variable with the smallest coefficient

• The variable with the largest coefficient

What should you do if the coefficients of the variable you want to eliminate are not directly cancelable?

• Multiply one or both equations by a constant to make the coefficients cancelable

• Ignore the variable and move to the next one

• Divide the equations by the coefficients

• Add a new equation to the system

After eliminating one variable, what is the next step?

• Multiply the new equations by a constant

• Check for consistency in the original equations

• Reintroduce the eliminated variable

• Solve the remaining system of two variables

How do you solve the system of two variables obtained after elimination?

• By multiplying the equations by a constant

• By adding a third variable

• By using the substitution or addition method

• By graphing the equations

What is the substitution method?

• Adding the equations together

• Multiplying the equations by a constant

• Isolating one variable and substituting its value into the other equation

• Replacing one variable with another

What do you do after finding the values of x and y?

• Re-eliminate one of the variables

• Multiply the solutions by a constant

• Find the value of z using one of the original equations

• Check the solutions in the original equations

How do you find the value of z?

• By adding the values of x and y

• By substituting the values of x and y into one of the original equations

• By eliminating x and y from the equations

• By graphing the equations

What is the final step in solving the system of equations?

• Multiply all solutions by a constant

• Verify the solution by substituting back into the original equations

• Divide the solutions by the coefficients

• Add all solutions together

What is the correct order of the solution set?

• (y, x, z)

• (x, y, z)

• (z, x, y)

• (x, z, y)