Monday, August 27, 2012

Introduction to solve by elimination method


Introduction to solve by elimination method

This is one of the methods used to calculate the unknowns involved in different simultaneous equations. Here we need to have equations equal to the number of unknowns. Now, let us discuss the elimination method by solving few simultaneous equations of two unknowns.
Example to Solve by Elimination Method

Ex 1: Solve the following simultaneous equations using elimination method

          3x + 2y = 18

          4x – y = 2

Sol:  Here let us call the equations as 1 and 2.

         3x + 2y = 18 ---------`|->` (1)

         4x – y = 2------------`|->` (2)

(2) × 2  `rArr` 8x – 2y = 4

(+) (1)  `rArr` 3x + 2y = 18

         `rArr` 11x      = 22

          `rArr`   x = `(22)/(11)` = 2

                   x = 2

Now plug in x = 2 in the equation number (1) as follows:

3x + 2y = 10   `rArr` 3(2) + 2y = 18

                      `rArr` 2y = 18 - 6 = 12

                      `rArr` y = `(12)/(2)` = 6.

                      `rArr` y = 6

Therefore, the solution of the given equations are x = 2, y = 6.
Example to Solve by Elimination Method

Ex 2: Solve the following simultaneous equations using elimination method

          3x + 2y = 23

           x – y = 1

Sol:  Here let us call the equations as 1 and 2.

         3x + 2y = 23 ---------à (1)

          x – y = 1------------à (2)

(2) × 2  `rArr` 2x – 2y = 2

(+) (1)  `rArr` 3x + 2y = 23

         `rArr` 5x   = 25

         `rArr` x = `(25)/(5)` = 5

                x = 5

Now plug in x = 5 in the equation number (1) as follows:

3x + 2y = 23 `rArr` 3(5) + 2y = 23

                   `rArr` 2y = 23 -15 = 8

                   `rArr`  y = `(8)/(2)` = 4

                   `rArr` y = 4.

Therefore, the solution of the given equations are x = 5, y = 4.
Practice Problems to Solve by Elimination Method

Solve the following simultaneous equations using elimination method:

(i) 4x + 3y = 10

        x + y = 3

Answer: x = 1, y = 2.

(i) 5x + 2y = 16

    3x + 4y = 18

Answer: x = 2, y = 3.

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