Interchanged Coefficients Method
Upasutra : Sankalana Vyavakalanaathyaam
Meaning : By addition and by subtraction
This sutra ( or upasutra ) is used when the x coefficients and the y coefficients are found interchanged. In this case the two equations are added and subtracted to obtain two simple simultaneous equations which on solving yield x and y.
Consider the following equations :
1) 43x - 21y = 129
21x - 43y = 63
On adding, 64x -64y = 192
--> x-y = 192/64 = 3
On subtracting, 22x + 22y = 66
--> x + y = 66/22 = 3
--> x + y = 3 and x - y = 3
--> x = 3 and y = 0.
2) 23x - 13y = 270
13x - 23y = 90
On adding, 36x - 36y = 360
--> x - y = 10
On subtracting, 10x + 10y = 180
--> x + y = 18
Hence on solving the following equations we get x = 14 , y = 4.