Solve for x and y :
` 152 x - 378 y = - 74, - 378 x + 152 y = - 604 `

Explanation

The given equations are
` 152 x - 378 y = - 74 " "`… (i)
` - 378 x + 152 y = - 604" " `…(ii)
Clearly, the coefficients of x and y in one equation are intercharged in the other.
Adding (i) and (ii), we get
` { 152 + (- 378)}x + {(-378) + 152 } y = - ( 74 + 604) `
` rArr ( - 226)x + ( - 226) y = - 678 `
`rArr ( - 226) (x + y ) = - 678 `
` rArr (x + y ) = (-678)/(- 226) rArr x + y = 3" " `... (iii)
Subtracting (ii) from (i), we get
`( 152 + 378) x + ( - 378 - 152 ) y = (-74 + 604) `
` rArr 530 x - 530 y = 530 `
`rArr 530 ( x- y ) = 530 rArr x - y = 1 " " `... (iv)
Adding (iii) and (iv), we get ` 2x = 4 rArr x = 2`.
Substracting (iv) from (iii), we get `2y = 2 rArr y = 1 `
Hence, ` x = 2 and y = 1`.