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

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 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).

Related Terms for Elimination Method

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Equation