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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