In system of linear equations in algebra the elimination method is one of the important methods in solving the equations for the variables. The elimination method is done by addition of the given two equations where one of the variables may eliminate and the other variables can be determined by substituting in the equation. Now we see about addition elimination method.

Now we are going to see the steps for solving the addition of elimination method as follows,

The given two equations are taken.

Then, add the two equations where one of the variables will be eliminated.

Then, by substituting the value in another equation the variable value can be determined.

Example 1:

Solve the given equation by addition of elimination method:

x + y = 8

- x + 2y = 4

Solution:

First we have to take the both equations

x + y = 8

-x + 2y = 4

Now solve the equation by adding them by elimination method.

x + y = 8

- x + 2y = 4

-----------------

3y = 12

------------------

Let us divide the equation by 3,

y = 12

y = `12/3`

y = 4

Put the value of y in the equation we get,

x + y = 8

x + 4 = 8

x = 8 – 4

x = 4.

The value of x and y are determined as 4 and 4 respectively.

Example 2:

Solve the equation by addition of elimination method:

2x + 4y = 8

x - 4y = 4

Solution:

First we have to take the both equations

2x + 4y = 8

x - 4y = 4

Now solve the equation by adding them by elimination method.

2x + 4y = 8

x - 4y = 4

-----------------

3x      = 12

------------------

Divide the equation by 3,

x = 12

x = `12/3`

x = 4

Put the value of x in the equation we get,

2x + 4y = 8

2(4) + 4y = 8

8 + 4y = 8

4y = 8 - 8

y = 0.

The value of x and y are determined as 4 and 0 respectively.