Simultaneous Equations Using Elimination Method

Introduction


The elimination method is one way to solve simultaneous equation. It is very useful really if the coeeficients of the equation are greater than one you. Let's proceed to see how this method can be used.

Solve the following simultaneous equation, 3a-4b= 1, 2a+3b= 5

(1.) 3a-4b=0, 2a+3b= 5

Solution

Name the equations

3a-4b= 1                                        (1)

2a+3b= 5                                       (2)

Then multiply eqn (1) by 2 and eqn (2) by 3

(3a-4b= 1)*2 and

(2a+3b= 5)*3 to give

6a-8b= 2                                          (3)

6a+9b=15                                        (4)

Subtract eqn (3) from (4)

6a+9b= 15

-

6a-8b= 2

17b= 13

b= 13/17

Substitute for b in (1).

So from (1)

3a-4b= 1

and since b= 13/17

3a-4(13/17)=1

3a-4.13/17= 1

3a-52/17= 1

3a= 1+52/17

3a= 17/1+52/17

3a= (17+52)/17

3a= 69/17

a= 69/17*1/3

a= 23/17

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