ELIMINATION METHOD

In this page elimination method we are going to see how to solve any linear equation by using this method.

Steps in Elimination Method

In the given linear equations we can eliminate any one of the variables.

The flow chart given below represents what are the steps to be done in this method.

Example problems

Let us consider the example below to understand this topic better

Question 1 :

Solve by elimination method

3 x + 4 y = -25

2 x - 3 y = 6

Solution:

3 x + 4 y = -25 ---- (1)

2 x - 3 y = 6  ---- (2)

Since the coefficients are different we have to find the common number for 4 and 3.The common number for 4 and 3 is 12.

(1) x 3 => 9 x + 12 y = -75

(2) x 4 => 8 x - 12 y = 24

Since the signs are different we have to add equation for eliminating y.

(1) + (2)         9 x + 12 y = -75

                       8 x - 12 y = 24

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

                        17 x = - 51

                             x = -51/17

                             x = -3

substitute x = -3 in the first equation

           3 (-3) + 4 y = -25

             - 9 + 4 y = -25 

                     4 y = -25 + 9

                     4 y = -16

                        y = -16/4

                        y = -4

Solution:

      x = -3

      y= -4

We can also verify the solution which we have found by applying these values in any of the given original equation

          3 (-3) + 4 (-4) = -25

              -9 - 16 = -25

                   - 25 = -25

So we can decide the answer what we got is correct.

Question 2 :

Solve by elimination method

2 x + 3 y = 5

3 x + 4 y = 7

Solution:

2 x + 3 y = 5  ---- (1)

3 x + 4 y = 7  ---- (2)

The coefficients of x and y are different.The symbols of x terms and y terms are same.So we can eliminate either x or y term.

So,we are going to eliminate "y" for that we have to find the L.C.M for 3 and 4.The L.C.M for 3 and 4 is 12.

(1) x 4 => 8 x + 12 y = 20

(2) x 3 => 9 x + 12 y = 21

Since the signs are same we have to subtract the 2nd equation from 1st equation equation for eliminating y.

(1) - (2)          8 x + 12 y = 20

                      9 x + 12 y = 21

                      (-)    (-)      (-)

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

                        -1 x = - 1

                             x = -1/(-1)

                             x = 1

substitute x = 1 in the first equation

          8 (1) + 12 y = 20

             8 + 12 y = 20 

                     12 y = 20 - 8

                     12 y = 12

                        y = 12/12

                        y = 1

Solution:

      x = 1

      y = 1

We can also verify the solution which we have found by applying these values in any of the given original equation

          8 x + 12 y = 20

          8(1) + 12 (1) = 20

                 20 = 20

So we can decide the answer what we got is correct.

Elimination method worksheet contains some practice questions based on this topic.You can also try that.


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