Question

Solve the pair of linear equations: 152x - 378y = – 74, -378x +152y = – 604.

Answer 1

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
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-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]
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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..