Elimination Method Mean in Math?

The elimination method using solving a system of linear equations algebraically is the most widely used method out of all the methods to solve linear equations.

 In the elimination method, we eliminate any one of the unknown variables by using basic arithmetic operations and then simplify the equation to find the value of the other unknown variable. Then we can put that value in any of the equations to find the value of the variable eliminated.

The elimination method is very simple and easy to use because here we eliminate one of the terms that make our calculations simple. In this article, we will learn to solve the systems of linear equations by using the elimination method. We shall solve various examples based on the concept for a better understanding.

What is an Elimination Method?

 The definition of the elimination method is about eliminating one of the terms containing any of the variables to make the calculations easier.

This is done by dividing or multiplying a number by the equation(s) such that the coefficients of any one of the variable terms become the same.

Then, we subtract or add both the equations to eliminate or remove that term from the result. The elimination method is called the addition method. For example, solve these two linear equations containing two variables by the elimination method.

Solving the system of linear equations by using the elimination method?

The elimination method is used to solve systems of linear equations of two variables by eliminating a variable and calculating the value of the variable to find the solution. Using the elimination method to solve a system of linear equations with two variables.

 Consider two linear equations

 2x-y=8..>(1)

X+Y=1..>(2)

Solution:

2x-y=8..>(1)

X+Y=1..>(2)

Add equations (1) and (2)

3x=9

X=9/3

X=3

Put the value of x in equation 2

3+y=1

Y=1-3

Y=-2

X=3 and y=-2

Step solve the system of linear equations by using the elimination Method

The elimination method is useful to solve a system of linear equations with two or three variables. We can solve three equations as well using this method. But it can only be applied to two equations at a time. steps to solve a system of linear equations using the elimination method

Step-1: The first step is to divide or multiply both the linear equations with a non-zero number to get a common coefficient of any one of the variables in both equations.

Step-2: subtract or add both the equations such that the same terms will get eliminated.

Step-3: Simplify the result to get a final result of the left out variable (let’s say, y) such that we will only get an answer in the form of y=c, where c is any constant.

Step-4: At last, substitute this value of a variable in any of the given equations to find the value of the other given variable

For example:

Considered two linear equation

x+y=5..>(1)      

2x-3y=5..> (2)

Solution:

x+y=5..>(1)      

2x-3y=5..> (2)

Multiplying 2 by equation (1) on both side

2x+2y=10…>(3)

Subtract equation 2 from 3

Put the value of y in equation (1)

x+y=5

x+1=5

x=5-1

x=4

x=4 and y=1

Summary

The elimination method is used to solve a system of linear two or three-variable equations.

This method is simple and easy and makes the calculations easier as it eliminates one variable and hence, reduces the calculations.

We make the coefficient of a variable identical to eliminate the corresponding variable

There are various ways of solving linear equations in two variables like the graphical method, the substitution method, the elimination method, and the determinant method. The cross multiplication method.