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CBSE Class 10 Answered

<div> <p class="MsoListParagraph" style="text-indent: -.25in; mso-list: l0 level1 lfo1;"><!--[if !supportLists]--><span style="font-size: 16.0pt; mso-bidi-font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">1.<span style="font-size: 7pt; line-height: normal; font-family: 'Times New Roman';">&nbsp;&nbsp;&nbsp; </span></span><!--[endif]--><span style="font-size: 12.0pt; line-height: 115%;">If am </span><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">&Dagger; bl , then the system of equations :</span><span style="font-size: 12.0pt; line-height: 115%;"></span></p> <p class="MsoNormal"><span style="font-size: 12.0pt; line-height: 115%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ax + by = c </span></p> <p class="MsoNormal"><span style="font-size: 12.0pt; line-height: 115%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; lx +my = n </span></p> <p class="MsoListParagraphCxSpFirst" style="margin-left: 63.75pt; mso-add-space: auto; text-indent: -.25in; mso-list: l1 level1 lfo2;"><!--[if !supportLists]--><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">(a)<span style="font-size: 7pt; line-height: normal; font-family: 'Times New Roman';">&nbsp;&nbsp; </span></span><!--[endif]--><span style="font-size: 12.0pt; line-height: 115%;">has a unique solution .</span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-left: 63.75pt; mso-add-space: auto; text-indent: -.25in; mso-list: l1 level1 lfo2;"><!--[if !supportLists]--><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">(b)<span style="font-size: 7pt; line-height: normal; font-family: 'Times New Roman';">&nbsp;&nbsp; </span></span><!--[endif]--><span style="font-size: 12.0pt; line-height: 115%;">has no solution .</span></p> <p class="MsoListParagraphCxSpMiddle" style="margin-left: 63.75pt; mso-add-space: auto; text-indent: -.25in; mso-list: l1 level1 lfo2;"><!--[if !supportLists]--><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">(c)<span style="font-size: 7pt; line-height: normal; font-family: 'Times New Roman';">&nbsp;&nbsp;&nbsp; </span></span><!--[endif]--><span style="font-size: 12.0pt; line-height: 115%;">has infinitely many solutions.</span></p> <p class="MsoListParagraphCxSpLast" style="margin-left: 63.75pt; mso-add-space: auto; text-indent: -.25in; mso-list: l1 level1 lfo2;"><!--[if !supportLists]--><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">(d)<span style="font-size: 7pt; line-height: normal; font-family: 'Times New Roman';">&nbsp;&nbsp; </span></span><!--[endif]--><span style="font-size: 12.0pt; line-height: 115%;">may and may not have solutions.</span></p> </div>
Asked by utkarshdristant1998 | 03 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 | 04 Jun, 2014, 10:13: AM
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