ICSE Class 9 Answered

11) If the following three equations hold simultaneously for x and y , find p.

3x+7y+5=0

4x-3y-8=0

Px+y-1=0

22) Can the following equations hold simultaneously? If so, find the valuesof x and y.

x/12+y/15=1

5x-2y=6

3x+5y=59.4

Asked by BHAVANA BHAT | 11 Jul, 2014, 05:35: PM

Expert Answer

$11 right parenthesis 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 r q u a t i o n s : 3 x plus 7 y equals minus 5... left parenthesis 1 right parenthesis 4 x minus 3 y equals 8... left parenthesis 2 right parenthesis P x plus y equals 1... left parenthesis 3 right parenthesis M u l t i p l y space t h e space e q u a t i o n space left parenthesis 1 right parenthesis space b y space 3 space a n d space e q u a t i o n space left parenthesis 2 right parenthesis space b y space 7 comma space w e space h a v e 9 x plus 21 y equals minus 15... left parenthesis 3 right parenthesis 28 x minus 21 y equals 56... 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 37 x equals 41 rightwards double arrow x equals 41 over 37... left parenthesis 5 right parenthesis 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 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 3 cross times open parentheses 41 over 37 close parentheses plus 7 y equals minus 5 rightwards double arrow 123 over 37 plus 7 y equals minus 5 rightwards double arrow 7 y equals minus 5 minus 123 over 37 rightwards double arrow 7 y equals fraction numerator minus 185 minus 123 over denominator 37 end fraction rightwards double arrow 7 y equals fraction numerator minus 308 over denominator 37 end fraction rightwards double arrow y equals fraction numerator minus 44 over denominator 37 end fraction... left parenthesis 6 right parenthesis N o w space c o n s i d e r space t h e space e q u a t i o n space P x plus y minus 1 equals 0 S u b s t i t u t i n g space t h e space v a l u e s space o f space x space a n d space y space f r o m space e q u a t i o n s space left parenthesis 5 right parenthesis space a n d space left parenthesis 6 right parenthesis space i n space t h e space a b o v e space e q u a t i o n comma space w e space h a v e comma P cross times 41 over 37 fraction numerator minus 44 over denominator 37 end fraction minus 1 equals 0 rightwards double arrow fraction numerator 41 P over denominator 37 end fraction fraction numerator minus 44 over denominator 37 end fraction minus 37 over 37 equals 0 rightwards double arrow 41 P minus 81 equals 0 rightwards double arrow 41 P equals 81 rightwards double arrow P equals 81 over 41 left parenthesis 22 right parenthesis 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 : x over 12 plus y over 15 equals 1... left parenthesis 1 right parenthesis 5 x minus 2 y equals 6... 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 fraction numerator 60 x over denominator 12 end fraction plus fraction numerator 60 y over denominator 15 end fraction equals 60 rightwards double arrow 5 x plus 4 y equals 60... left parenthesis 3 right parenthesis S u b s t r a c t i n g space e q u a t i o n space left parenthesis 2 right parenthesis space f r o m space left parenthesis 3 right parenthesis comma space w e space h a v e comma 6 y equals 54 rightwards double arrow y equals 54 over 6 rightwards double arrow y equals 9 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 y space i n space e q u a t i o n space left parenthesis 2 right parenthesis comma space w e space h a v e 5 x minus 2 cross times 9 equals 6 rightwards double arrow 5 x minus 18 equals 6 rightwards double arrow 5 x equals 6 plus 18 rightwards double arrow 5 x equals 24 rightwards double arrow x equals 24 over 5 rightwards double arrow x equals 4.8 N o w space s u b s t i t u t i n g space t h e space v a l u e s space o f space x space a n d space y space i n space t h e space l e f t space h a n d s i d e space o f space t h e space g i v e n space e q u a t i o n space 3 x plus 5 y equals 59.4 comma space w e space h a L. H. S equals 3 cross times 4.8 plus 5 cross times 9 rightwards double arrow L. H. S equals 14.4 plus 45 rightwards double arrow L. H. S equals 59.4 rightwards double arrow L. H. S space equals R. H. S H e n c e space t h e space s o l u t i o n space s e t space s a t i s f i e s space a l l space t h e space t h r e e space e q u a t i o n s.$