Solve the pair of linear equations: 152x - 378y = – 74, -378x +152y = – 604.
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When the coefficients of x and y in one equation interchanged in the other:
Step 1. Add the given equations and from it obtain an equation of the form x+ y = a.
Step 2. Subtract the given equations and from it obtain an equation of the form x -y = b.
Now , x+y = a and x- y = b can be solved easily.
SOLUTION:
152x - 378y = – 74………….(1)
-378x +152y = – 604………..(2)
Adding Equation 1 and 2
152x - 378y = – 74
-378x +152y = – 604
-----------------------------
-226x -226y = - 678
-226(x+y ) = -678
x+y = -678/-226= 3
x + y = 3……………….(3)
Subtracting equation 1 and 2
152x - 378y = – 74
-378x +152y = – 604
(+) (-) (+)
-----------------------------
530x - 530y = 530
530 (x- y ) = 530
x-y = 530/530= 1
x - y = 1……………….(4)
On adding equation 3 and 4
x + y = 3
x - y = 1 [By elimination method]
--------------
2x = 4
x = 4/2
x = 2
On substituting x =2 in eq 3
x + y = 3
2 + y = 3
y = 3-2
y = 1
Hence , x= 2 and y= 1 is the required solution.
HOPE THIS WILL HELP YOU..
Step 1. Add the given equations and from it obtain an equation of the form x+ y = a.
Step 2. Subtract the given equations and from it obtain an equation of the form x -y = b.
Now , x+y = a and x- y = b can be solved easily.
SOLUTION:
152x - 378y = – 74………….(1)
-378x +152y = – 604………..(2)
Adding Equation 1 and 2
152x - 378y = – 74
-378x +152y = – 604
-----------------------------
-226x -226y = - 678
-226(x+y ) = -678
x+y = -678/-226= 3
x + y = 3……………….(3)
Subtracting equation 1 and 2
152x - 378y = – 74
-378x +152y = – 604
(+) (-) (+)
-----------------------------
530x - 530y = 530
530 (x- y ) = 530
x-y = 530/530= 1
x - y = 1……………….(4)
On adding equation 3 and 4
x + y = 3
x - y = 1 [By elimination method]
--------------
2x = 4
x = 4/2
x = 2
On substituting x =2 in eq 3
x + y = 3
2 + y = 3
y = 3-2
y = 1
Hence , x= 2 and y= 1 is the required solution.
HOPE THIS WILL HELP YOU..
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