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: 
[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).
Quick Summary
- Multiply equations to make coefficients of one variable opposites.
- Add equations to eliminate that variable.
- Solve for the remaining variable.
- Substitute back to find the value of the eliminated variable.
🍎 Teacher Insights
Emphasize the importance of organizing work clearly. Encourage students to check their solutions. Provide practice with various types of equations.🎓 Prerequisites
- Basic Algebra
- Solving Linear Equations
- Understanding Variables
Check Your Knowledge
Q1: Solve the following system of equations using the elimination method: x + y = 5, x - y = 1
Q2: What is the first step in solving 2x + 3y = 7 and 4x - y = 1 using the elimination method to eliminate x?
Frequently Asked Questions
Q: When is the elimination method most useful?
A: When the coefficients of one variable are easily made opposites or are already opposites.
Q: Can the elimination method be used for systems with more than two variables?
A: Yes, but it requires eliminating variables systematically to reduce the system to a solvable form.