Solve for x & y using elimination method:-
(i)2 left parenthesis a x minus b y right parenthesis minus left parenthesis a plus 4 b right parenthesis equals 0 2 left parenthesis b x plus a y right parenthesis plus left parenthesis b minus 4 a right parenthesis equals 0
 
(ii)x over a plus y over b equals 2 a x minus b y equals a squared minus b squared

Asked by araima2001 | 2nd Jun, 2015, 02:43: PM

Expert Answer:

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

Answered by Vimala Ramamurthy | 3rd Jun, 2015, 08:50: AM

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