Solving Three Variable Systems with Elimination

________________ is a set of two or more equations that have the same variables.

• solution of a system

• elimination method

• system of equations

• table

a method to solving a system of equations by getting rid of one of the variables first to solve for the other variable. 

• Systems by Graphing

• Systems by Substitution

• Systems by Elimination

• Systems by Drawing

Find the solution to the following system of equations using the elimination method: 2x + 3y - z = 5 3x - 2y + 4z = 7 4x + y + 2z = 3

• x = 2, y = -1, z = 1

• x = -2, y = 1, z = -1

• x = 1, y = 2, z = -1

• x = 3, y = -2, z = 2

Solve the system using elimination.

Solve the system of equations using the elimination method: 3x + 2y - z = 6 2x - y + 3z = 4 4x + 3y + 2z = 9

• x = 4/5, y = 2, z = -3/5

• x = 0, y = 0, z = 0

• x = -2/3, y = 1/2, z = 1/4

• x = 1, y = 3, z = 2

Solve the system using elimination.

Which of the following could be a correct first step in solving the system shown? Select all that apply.

• Multiply the first equation by 2, then add the result to the third equation.

• Multiply the second equation by 2, then add the result to the third equation.

• Add the first and second equation.

• Add the first and third equation.

• Add the second and third equation.

Solve the system of equations using the elimination method:

3x + 2y - z = 6

2x - y + 3z = 4

4x + 3y + 2z = 9

• x = 4/5, y = 2, z = -3/5

• x = 0, y = 0, z = 0

• x = -2/3, y = 1/2, z = 1/4

• x = 1, y = 3, z = 2