InterviewSolution
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Solve for x and y : ` 152 x - 378 y = - 74, - 378 x + 152 y = - 604 ` |
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Answer» 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`. |
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