Method 12

Solution of some simultaneous equations

This method is based on the sutra " Anurupye Sunyamanyat " which means ' If one is in the ratio the other one is zero ' .

Explaining the method by an example

Example 1 : - Find the solution of the following simultaneous equation .
3x + 7y = 2
4x + 21y = 6

Answer : -

In above we notice that the cofficients of y are in the same ratio as the constants .
i.e.

7 : 21 = 2 : 6 = 1 : 3

Hence Sutra says that if one is in the ratio the other one is zero .
So x =0
and
7.y = 2 => y = 2 / 7


Example 2 : - Find the solution of the following simultaneous equation .
12x + 78y = 12
16x + 96y = 16

Answer : -

In the above we see that
12 : 16 = 12 : 16

Hence y = 0 and
12 .x = 12
=> x =1


Example 3 : - Find the solution of the following simultaneous equation .
a.x + b.y = 2.b.m
c.x + d.y = 2.d.m

Answer : -

In the above we see that cofficients of y are in the same ratio as constants

b : d = 2.b.m : 2.d.m = b : d

Hence according to the sutra
x = 0 and
b.y = 2.b.m
=> y = 2.m