Archive
9th of September 2015
Mathematics
Q:

solve for x and y : 5 / x -1 + 1 / y -2 = 2 ; 6 / x-1 - 3/y-2 =1.

Nisha_vini29 - CBSE - Class X

Monday, September 07, 2015 at 21:47:PM

A:

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 5 over denominator x minus 1 end fraction plus fraction numerator 1 over denominator y minus 2 end fraction equals 2 A n d comma space fraction numerator 6 over denominator x minus 1 end fraction minus fraction numerator 3 over denominator y minus 2 end fraction equals 1 S u b s t i t u t i n g space X equals fraction numerator 1 over denominator x minus 1 end fraction space a n d space Y equals fraction numerator 1 over denominator y minus 2 end fraction comma space w e space h a v e comma 5 X plus Y equals 2... left parenthesis 1 right parenthesis 6 X minus 3 Y equals 1... 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 3 comma space w e space h a v e comma 15 X plus 3 Y equals 6... 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 21 X equals 7 rightwards double arrow X equals 7 over 21 rightwards double arrow X equals 1 third rightwards double arrow fraction numerator 1 over denominator x minus 1 end fraction equals 1 third rightwards double arrow x minus 1 equals 3 rightwards double arrow x equals 3 plus 1 rightwards double arrow x equals 4 S u b s t i t u t i n g space X equals 1 third 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 5 X plus Y equals 2 rightwards double arrow 5 cross times 1 third plus Y equals 2 rightwards double arrow Y equals 2 minus 5 over 3 rightwards double arrow Y equals fraction numerator 6 minus 5 over denominator 3 end fraction rightwards double arrow Y equals 1 third rightwards double arrow fraction numerator 1 over denominator y minus 2 end fraction equals 1 third rightwards double arrow y minus 2 equals 3 rightwards double arrow y equals 3 plus 2 rightwards double arrow y equals 5

Wednesday, September 09, 2015 at 18:08:PM