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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.

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)

Solution:

Step 1: [Add the first two equations to eliminate y.]
Step 2: [Add the second and third equations to eliminate y.]
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 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).

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