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Find the values of a and b for which the following system of linear equation has an infinite number of solutions.

2x - 3y = 7, ( a + b )x - ( a + b - 3 )y = 4a + b

Asked by Sayantani Ghosh | 5th Jun, 2014, 04:06: PM

Expert Answer:

$2 x space minus space 3 y space equals space 7 left parenthesis a plus b right parenthesis x space minus space left parenthesis a plus b minus 3 right parenthesis y space equals space 4 a space plus space b f o r space i n f i n i t e space s o l u t i o n s space b o t h space e q u a t i o n s space s h o u l d space b e space s i m i l a r comma space i n space o r d e r space t o space b e space s i m i l a r space f o l l o w i n g space c o n d i t i o n s space m u s t space s a t i s f y a plus b space equals space 2 n space space space space space space space space open parentheses 1 close parentheses a plus b minus 3 space equals space 3 n space space space open parentheses 2 close parentheses 4 a plus b equals 7 n space space space space space space space space space open parentheses 3 close parentheses S o l v i n g space 1 space a n d space 2 space w e space g e t 2 n space minus 3 space equals space 3 n s o comma space n space equals space minus 3 s o space w e space g e t space a plus b equals minus 6 space space space space space space space space space open parentheses 4 close parentheses 4 a plus b equals minus 21 space space space space space space open parentheses 5 close parentheses S o l v i n g space 4 space a n d space 5 space w e space g e t comma space 3 a equals minus 21 plus 6 equals minus 15 a equals space minus 5 space s o space b space equals space minus 1 left parenthesis a comma space b right parenthesis space equals space left parenthesis minus 5 comma space minus 1 right parenthesis$

Answered by Dharma Teja | 6th Jun, 2014, 07:24: PM

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