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For no solution (2p-1)x+(p-1)y=2p+1&y+3x+1=0 |
| Answer» For (2p - 1)x + (p - 1 )y - (2p + 1) = 0{tex}a _ { 1 } = 2 p - 1 , b _ { 1 } = p - 1 \\text { and } c _ { 1 } = - ( 2 p + 1 ){/tex}and for\xa03x + y - 1 = 0{tex}a _ { 2 } = 3 , b _ { 2 } = 1 \\text { and } c _ { 2 } = - 1{/tex}The condition for no solution is{tex}\\frac { a _ { 1 } } { a _ { 2 } } = \\frac { b _ { 1 } } { b _ { 2 } } \\neq \\frac { c _ { 1 } } { c _ { 2 } }{/tex}{tex}\\frac { 2 p - 1 } { 3 } = \\frac { p - 1 } { 1 } \\neq \\frac { 2 p + 1 } { 1 }{/tex}By\xa0{tex}\\frac { 2 p - 1 } { 3 } = \\frac { p - 1 } { 1 }{/tex}3/7-3 = 2 /7 -13/7 - 2/7 = 3 - 1{tex}\\therefore {/tex}\xa0p = 1from\xa0{tex}\\frac { p - 1 } { 1 } \\neq 2 p + 1{/tex}We have\xa0{tex}p - 1 \\neq 2 p + 1 \\text { or } 2 p - p = - 1 - 1{/tex}{tex}p \\neq - 2{/tex}from\xa0{tex}\\frac{{2p - 1}}{3} \\ne \\frac{{2p + 1}}{1}{/tex}{tex}\\Rightarrow \\quad 2 p - 1 \\neq 6 p + 3{/tex}{tex} \\Rightarrow \\quad 4p \\ne - 4{/tex}{tex}p \\neq - 1{/tex} | |