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1.    If am ‡ bl , then the system of equations :

                            ax + by = c

                            lx +my = n

(a)   has a unique solution .

(b)   has no solution .

(c)    has infinitely many solutions.

(d)   may and may not have solutions.

Asked by utkarshdristant1998 | 3rd Jun, 2014, 03:43: PM

Expert Answer:

$G i v e n space t h a t space a m not equal to b l rightwards double arrow a over l not equal to b over m W e space k n o w space t h a t space i f a subscript 1 x plus b subscript 1 y plus c subscript 1 equals 0 a subscript 2 x plus b subscript 2 y plus c subscript 2 equals 0 i s space a space p a i r space o f space l i n e a r space e q u a t i o n s space i n space t w o space v a r i a b l e s space x space a n d space y space s u c h space t h a t a subscript 1 over a subscript 2 not equal to b subscript 1 over b subscript 2 comma space t h e n space t h e space p a i r space o f space l i n e a r space e q u a t i o n s space i s space c o n s i s t e n t space w i t h space a space u n i q u e space s o l u t i o n. T h u s comma space t h e space g i v e n space s y s t e m space o f space e q u a t i o n s space i s space c o n s i s t e n t space w i t h space a space u n i q u e space s o l u t i o n space a n d space h e n c e space left parenthesis a right parenthesis space i s space t h e space c o r r e c t space o p t i o n.$

Answered by Vimala Ramamurthy | 4th Jun, 2014, 10:13: AM

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