**Definition of Elimination Method**

- Elimination Method is the process of eliminating one of the variables in a system of equations using addition or subtraction in conjunction with multiplication or division and solving the system of equations.

**Solved Example on Elimination Method**

Using the elimination method, solve the system of equations.

2x-y+ 3z= 9

x+y+z= 6

x-y+z= 2

Choices:

A. (2, 1, -1)

B. (4, 1, 1)

C. (1, -1, 2)

D. (1, 2, 3)

Correct Answer: D

Solution:

Step 1:[Add the first two equations to eliminatey.]

Step 2:[Add the second and third equations to eliminatey.]

Step 3:We now have a system of two equations in two variables:

Step 4:[Multiply the second equation with - 2 and add, and then solve forx.]

Step 5:So, 3x+ 4z= 15 givesz= 3 [Substitute the values.]

Step 6:x+y+z= 6 givesy= 2[Substitute the values.]

Step 7:So, the solution is (1, 2, 3).

**Related Terms for Elimination Method**

- Addition
- Subtraction
- Multiplication
- Division
- Equation