i cant understand the geometrical representation of linear equations in two variables

Asked by adityajhasaby0107 | 30th Nov, 2015, 08:17: PM

Expert Answer:

G e o m e t r i c a l space r e p r e s e n t a t i o n space o f space l i n e a r space e q u a t i o n s space i n space t w o space v a r i a b l e s space i s space t h e space p a i r space o f space t w o space s t r a i g h t space l i n e s. C o n s i d e r space t h e space s y s t e m space o f space e q u a t i o n s comma x plus 2 y equals 7 space a n d 4 x minus y equals 1 R e w r i t i n g space t h e space a b o v e space s y s t e m space o f space e q u a t i o n s comma space w e space h a v e comma y equals fraction numerator 7 minus x over denominator 2 end fraction... left parenthesis 1 right parenthesis a n d y equals 4 x minus 1 A s s u m e space d i f f e r e n t space v a l u e s space o f space x space a n d space c o m p u t e space t h e space c o r r e s p o n d i n g space v a l u e s space o f space y space u sin g space t h e space e q u a t i o n comma space y equals fraction numerator 7 minus x over denominator 2 end fraction L e t space u s space f o r m space t h e space f o l l o w i n g space t a b l e colon table row x 7 5 3 row y 0 1 2 end table P l o t space t h e space a b o v e space p o i n t s space i n space a space g r a p h space a n d space j o i n space t h e space p o i n t s space t o space f o r m space a space s t r a i g h t space l i n e.  S i m i l a r l y comma space a s s u m e space d i f f e r e n t space v a l u e s space o f space x space a n d space c o m p u t e space t h e space c o r r e s p o n d i n g space v a l u e s space o f space y space u s i n g space t h e space e q u a t i o n comma space y equals 4 x minus 1 L e t space u s space f o r m space t h e space f o l l o w i n g space t a b l e colon table row x 0 1 2 row y cell negative 1 end cell 3 7 end table P l o t space t h e space a b o v e space p o i n t s space i n space a space g r a p h space a n d space j o i n space t h e space p o i n t s space t o space f o r m space a space s t r a i g h t space l i n e.  F r o m space t h e space g r a p h space i t space i s space c l e a r space t h a t space t h e space t w o space s t r a i g h t space l i n e s space i n t e r s e c t space a t space t h e space p o i n t space open parentheses 1 comma 3 close parentheses.

Answered by Vimala Ramamurthy | 1st Dec, 2015, 01:08: PM