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(p-3)x+3y=ppx+py=12 |
| Answer» Consider equations (p - 3)x + 3y = pand px + py = 12For infinitely many solutions,{tex}\\frac{p - 3}{p}{/tex}\xa0=\xa0{tex}\\frac{3}{p}{/tex}\xa0=\xa0{tex}\\frac{p}{12}{/tex}...........(i)Consider,\xa0{tex}\\frac{3}{p}{/tex}\xa0=\xa0{tex}\\frac{p}{12}{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0p2 = 36 {tex}\\Rightarrow{/tex}\xa0p =\xa0{tex}\\pm{/tex}6For p = 6, from (i)\xa0{tex}\\frac{3}{6}{/tex}\xa0=\xa0{tex}\\frac{3}{6}{/tex}\xa0=\xa0{tex}\\frac{6}{12}{/tex}, trueFor p = -6, from (i)\xa0{tex}\\frac{-9}{-6}{/tex}\xa0=\xa0{tex}\\frac{3}{-6}{/tex}\xa0=\xa0{tex}\\frac{-6}{12}{/tex}, false.Hence, for p = 6, pair of linear equations has infinitely many solutions. | |