Elimination Method

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.

Video Examples: Algebra - Solving Systems of Equations - Elimination Method


Solved Example on Elimination Method

Ques: 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: Elimination Method [Add the first two equations to eliminate y.]
    Step 2:Elimination Method [Add the second and third equations to eliminate y.]
    Step 3: We now have a system of two equations in two variables: Elimination Method
    Step 4: Elimination Method [Multiply the second equation with - 2 and add, and then solve for x.]
    Step 5: So, 3x + 4z = 15 gives z = 3 [Substitute the values.]
    Step 6: x + y + z = 6 gives y = 2 [Substitute the values.]
    Step 7: So, the solution is (1, 2, 3).