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# By Addition and By Subtraction

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By Addition and By Subtraction sutra refers to the mental process of comparison.In comparing two things we look for similarities (addition) and differences (subtraction) between themThis sutra is helpful in solving  Simultaneous linear equations where the co-efficients of  x and y are interchanged

Example 1 :
25x - 17 y = 91
17x - 25 y = 35

Adding ( +) the co-efficients of x and y together,we get
42 x - 42 y = 126
42 (x - y ) = 126
x - y = 126 / 42
x - y = 3
Let x - y = 3 be -----> equation 1

Subtracting (-) the co-efficients of x and y together,we get
8 x +8 y =56
8(x+y) = 56
x + y = 56 / 8
x + y = 7
Let x + y =7 be -----> equation 2

Again, adding equation 1 and equation 2, we get
x - y + x + y = 3 + 7
2x = 10
Therefore , x = 5

Now subtracting equation 1 and equation 2 , we get
x - y - ( x +y) = 3 - 7
x - y - x - y = -4
-2y=-4
Therefore , y = 4

Result : (x,y) = (5,4)

Example 2 :
5x – 21y = 26
21x – 5y = 26

Adding ( +) the co-efficients of x and y together,we get
26x -26y = 52
x - y = 2 ----->equation 1

Subtracting (-) the co-efficients of x and y together,we get
5x -21 y - 21x+5y =0
-16x -16y = 0
x + y = 0 ---->equation 2

Again, adding equation 1 and equation 2,we get
2x = 2
Therefore x = 2
Now, subtracting equation 1 and equation 2,we get
-2y =0
Therefore y = 0

Result (x , y) = (2 , 0 )

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