SOLVE THE FOLLOWINGS O L V E space T H E space P A I R space O F space L I N E A R space E Q U A T I O N S semicolon left parenthesis 1 right parenthesis space space space space space fraction numerator 6 over denominator X plus Y end fraction space space space equals space space fraction numerator 7 over denominator X minus Y space end fraction space space plus 3 space space space A N D space space space fraction numerator 1 over denominator 2 left parenthesis X plus Y right parenthesis end fraction equals space fraction numerator 1 over denominator 3 left parenthesis X minus Y right parenthesis end fraction   left parenthesis 2 right parenthesis space fraction numerator 1 over denominator 2 left parenthesis X plus 2 Y right parenthesis end fraction plus fraction numerator 5 over denominator 3 left parenthesis 3 X minus 2 Y right parenthesis end fraction space equals space fraction numerator negative 3 over denominator 2 end fraction space space space space space space A N D space space space fraction numerator 5 over denominator 4 left parenthesis X plus 2 Y right parenthesis end fraction minus fraction numerator 3 over denominator 5 left parenthesis 3 X minus 2 Y right parenthesis end fraction equals 61 over 60

Asked by dalbirgolagarh | 24th Jul, 2015, 05:26: PM

Expert Answer:

1. C o n s i d e r space t h e space g i v e n space s y s t e m space o f space e q u a t i o n s colon fraction numerator 6 over denominator x plus y end fraction equals fraction numerator 7 over denominator x minus y end fraction plus 3..... left parenthesis 1 right parenthesis fraction numerator 1 over denominator 2 open parentheses x plus y close parentheses end fraction equals fraction numerator 1 over denominator 3 open parentheses x minus y close parentheses end fraction..... left parenthesis 2 right parenthesis  L e t space u equals fraction numerator 1 over denominator x plus y end fraction space a n d space v equals fraction numerator 1 over denominator x minus y end fraction T h u s comma space t h e space g i v e n space e q u a t i o n s space a r e colon 6 u equals 7 v plus 3... left parenthesis 3 right parenthesis u over 2 equals v over 3.... left parenthesis 4 right parenthesis R e w r i t i n g space t h e space a b o v e space e q u a t i o n s space w e space h a v e comma 6 u minus 7 v equals 3... left parenthesis 5 right parenthesis 3 u minus 2 v equals 0... left parenthesis 6 right parenthesis M u l t i p l y i n g space e q u a t i o n space left parenthesis 6 right parenthesis space b y space 2 space a n d space s u b t r a c t i n g space f r o m space e q u a t i o n space left parenthesis 5 right parenthesis comma space w e space h a v e comma minus 3 v equals 3 rightwards double arrow v equals negative 1 rightwards double arrow fraction numerator 1 over denominator x minus y end fraction equals negative 1 rightwards double arrow x minus y equals negative 1.... left parenthesis 7 right parenthesis S u b s t i t u t i n g space v equals negative 1 space i n space e q u a t i o n space left parenthesis 4 right parenthesis comma space w e space h a v e space u equals fraction numerator negative 2 over denominator 3 end fraction rightwards double arrow fraction numerator 1 over denominator x plus y end fraction equals fraction numerator negative 2 over denominator 3 end fraction rightwards double arrow x plus y equals fraction numerator negative 3 over denominator 2 end fraction... left parenthesis 8 right parenthesis A d d i n g space e q u a t i o n s space left parenthesis 7 right parenthesis space a n d space left parenthesis 8 right parenthesis comma space w e space h a v e comma 2 x equals fraction numerator negative 5 over denominator 2 end fraction rightwards double arrow x equals fraction numerator negative 5 over denominator 4 end fraction S u b s t i t u t i n g space t h e space v a l u e space x equals fraction numerator negative 5 over denominator 4 end fraction space i n space e q u a t i o n space left parenthesis 7 right parenthesis comma space w e space h a v e comma space fraction numerator negative 5 over denominator 4 end fraction minus y equals negative 1 rightwards double arrow fraction numerator negative 5 over denominator 4 end fraction plus 1 equals y rightwards double arrow y equals fraction numerator negative 1 over denominator 4 end fraction

Answered by Vimala Ramamurthy | 25th Jul, 2015, 11:45: AM

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