Question

Solve the following pair of linear equations by reducing it to another pair with smaller Coefficients.

2.

(i) 31x + 57y = 150

57x + 31y = 202

(ii) 152x -378y = -74

-378x +152y = -604.

Answer 1

( 1 ). 31x + 57y = 150-----------( 1 )
57x + 31y = 202---------------( 1 )

adding-----( 1 ) & -------( 2 ).

31x + 57y = 150
57x + 31y = 202
------------------------
88x + 88y = 352

x + y = 4----------( 3 )

subtracting-------( 1 ) & --------( 2 ).

31x + 57y = 150
57x + 31y = 202
(-)____(-)___(-)
------------------------
-26x + 26y = -52

x - y = 2---------( 4 )

from-------( 3 ) &------( 4 ).

x + y = 4
x - y = 2
-------------
2x = 6

x = 3 [ put in ------( 3 ) ]

x + y = 4

3 + y = 4

y = 4 - 3 = 1

x = 3 , y = 1







( 2 ) . 152x - 378y = -74------------( 1 )
-378x + 152y = -604-----------( 2 )

adding---------( 1 ) &----------( 2 )

152x - 378y = -74
-378x + 152y = -604
-----------------------------
-226x - 226y = -678

x + y = 3-------------( 3 )

subtracting-------( 1 ) & -------( 2 )

152x - 378y = -74
-378x + 152y = -604
(+)_____(-)____(+)
--------------------------------
530x - 530y = 530

x - y = 1-------------( 4 )

From---------( 3 ) & --------( 4 )

x + y = 3
x - y = 1
-------------
2x = 4

x = 2 [ put in --------( 3 ) ]

x + y = 3

2 + y = 3

y = 3 - 2 = 1

x = 2 , y = 1