Embarking on the mathematical journey of solving pairs of linear equations in two variables, the Elimination Method emerges as a strategic ally. As we dive into this method, Class 10 students will unravel the systematic approach and practical applications that make it a cornerstone of algebraic problem-solving.

Strategic Precision Mastering Algebraic Solutions with the Elimination Method

Understanding the Elimination Method

Make Coefficients Equal

• Multiply one or both equations to ensure the coefficients of one variable are the same or additive inverses.

Eliminate a Variable

• Add or subtract the modified equations to eliminate one variable, creating a new equation with a single variable.

Solve for the Variable

• Solve the new equation to find the value of the eliminated variable.

Back Substitution

• Substitute the found value back into one of the original equations to determine the value of the other variable.

Solving Linear Equations by Elimination Method

The elimination method is one of the techniques to solve the system of linear equations. In this method, either add or subtract the equations to get the equation in one variable. If the coefficients of one of the variables are the same, and the sign of the coefficients are opposite, we can add the equation to eliminate the variable. Similarly, if the coefficients of one of the variables are the same, and the sign of the coefficients are the same, we can subtract the equation to get the equation in one variable.In case, if we do not have the equation to directly add or subtract the equations to eliminate the variable, you can begin by multiplying one or both the equations by a constant value on both sides of an equation to obtain the equivalent linear system of equations and then eliminate the variable by simply adding or subtracting equations.

Download Science notes

Elimination Method Steps

Step 1: Firstly, multiply both the given equations by some suitable non-zero constants to make the coefficients of any one of the variables (either x or y) numerically equal.
Step 2: After that, add or subtract one equation from the other in such a way that one variable gets eliminated. Now, if you get an equation in one variable, go to Step 3. Else;

• If we obtain a true statement including no variable, then the original pair of equations has infinitely many solutions.
• If we obtain a false statement including no variable, then the original pair of equations has no solution, i.e., it is inconsistent.

Step 3: Solve the equation in one variable (x or y) to get its value.
Step 4: Substitute this value in any of the given equations to get the value of another variable

Advantages of the Elimination Method

Systematic Approach

• Offers a methodical step-by-step procedure, simplifying the solving process.

Versatility:

• Adaptable to various linear equations, making it a versatile tool in algebraic problem-solving.

Logical Reasoning

• Enhances logical reasoning as students manipulate equations to eliminate variables.

Quick Verification

• Allows for immediate verification of solutions by substituting them back into the original equations.

CBSE Class 10th Downloadable Resources: 

Being in CBSE class 10th and considering the board examinations you must be needing resources to excel in your examinations. At TestprepKart we take great pride in providing CBSE class 10th all study resources in downloadable form for you to keep you going. 

Below is the list of all CBSE class 10th Downloads available on TestprepKart for both Indian and NRI students preparing for CBSE class 10th in UAE, Oman, Qatar, Kuwait & Bahrain. 

SAMPLE PRACTICE QUESTION

Q1: What is the Elimination Method in solving systems of equations?

Ans: The Elimination Method is an algebraic technique for solving systems of linear equations by manipulating the equations to eliminate one variable when added or subtracted.

Q2: How does the Elimination Method start?

Ans: Begin by aligning the coefficients of one variable in both equations to be opposites, allowing elimination when the equations are combined.

Q3: Can the Elimination Method be applied to systems with more than two equations?

Ans: Yes, the Elimination Method is extendable to systems with more than two equations by systematically eliminating variables.

Q4: When is the Elimination Method preferred over other techniques?

Ans: The Elimination Method is advantageous when the coefficients of one variable can be easily manipulated to eliminate it, simplifying the system.

Q5: Are there scenarios where the Elimination Method might be less effective?

Ans: Yes, it may become less effective when coefficients are challenging to manipulate or when the system involves intricate algebraic expressions.

Download Question Bank