solve the following pairs of linear equations for x and y 
x/a + y/b = 2; ax-by=ax^2-bx^2
 

Asked by anshika adlakha | 24th Jun, 2014, 04:58: PM

Expert Answer:

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 space x over a plus y over b equals 2..... left parenthesis 1 right parenthesis a x minus b y equals a x squared minus b x squared..... left parenthesis 2 right parenthesis R e w r i t i n g space t h e space e q u a t i o n space left parenthesis 1 right parenthesis space a s b x plus a y equals 2 a b.... left parenthesis 3 right parenthesis M u l t i p l y i n g space t h e space e q u a t i o n space left parenthesis 2 right parenthesis space b y space apostrophe a apostrophe space a n d space t h e space e q u a t i o n space left parenthesis 3 right parenthesis space b y space apostrophe b apostrophe space w e space h a v e comma a squared x minus a b y equals a squared x squared minus a b x squared.... left parenthesis 4 right parenthesis b squared x plus a b y equals 2 a b squared...... left parenthesis 5 right parenthesis A d d i n g space e q u a t i o n s space left parenthesis 4 right parenthesis space a n d space left parenthesis 5 right parenthesis comma space w e space h a v e open parentheses a squared plus b squared close parentheses x equals a squared x squared minus a b x squared plus 2 a b squared rightwards double arrow open parentheses a squared minus a b close parentheses x squared minus open parentheses a squared plus b squared close parentheses x plus 2 a b squared equals 0 s o l v i n g space t h e space a b o v e space q u a d r a t i c space e q u a t i o n comma space w e space h a v e rightwards double arrow x equals fraction numerator open parentheses a squared plus b squared close parentheses plus-or-minus square root of open parentheses a squared plus b squared close parentheses squared minus 4 open parentheses a squared minus a b close parentheses cross times 2 a b squared end root over denominator 2 cross times open parentheses a squared minus a b close parentheses end fraction rightwards double arrow x equals fraction numerator open parentheses a squared plus b squared close parentheses plus-or-minus square root of open parentheses a squared plus b squared close parentheses squared minus 8 a cubed b squared plus 8 a squared b squared end root over denominator 2 cross times open parentheses a squared minus a b close parentheses end fraction S u b s t i t u t i n g space t h e space a b o v e space v a l u e space i n space e q u a t i o n space left parenthesis 3 right parenthesis comma space space w e space h a v e comma fraction numerator b open parentheses a squared plus b squared close parentheses plus-or-minus b square root of open parentheses a squared plus b squared close parentheses squared minus 8 a cubed b squared plus 8 a squared b squared end root over denominator 2 cross times open parentheses a squared minus a b close parentheses end fraction plus a y equals 2 a b rightwards double arrow a y equals 2 a b minus fraction numerator b open parentheses a squared plus b squared close parentheses plus-or-minus b square root of open parentheses a squared plus b squared close parentheses squared minus 8 a cubed b squared plus 8 a squared b squared end root over denominator 2 cross times open parentheses a squared minus a b close parentheses end fraction rightwards double arrow y equals 2 b minus fraction numerator b open parentheses a squared plus b squared close parentheses plus-or-minus b square root of open parentheses a squared plus b squared close parentheses squared minus 8 a cubed b squared plus 8 a squared b squared end root over denominator 2 a open parentheses a squared minus a b close parentheses end fraction

Answered by Vimala Ramamurthy | 25th Jun, 2014, 10:18: AM