Question

5/x - 6/y =-30 , 5/x + 4/y=20​

Answer 1

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

$\star{\sf{\orange{ \frac{5}{x} - \frac{6}{y} = - 30 }}}$

$\star \: {\sf{\orange{ \frac{5}{x} + \frac{4}{y} = 20}}}$

${\sf{\green{put \: \frac{1}{x} = p \: and \: \frac{1}{y}=q}}}$

$\implies{\sf{\blue{5p - 6q = - 30}}}.....(1)$

$\implies{\sf{\blue{5p + 4q = 20}}}....(2)$

${\sf{\underline{\red{Now \: from \: (1)}}}}$

$\implies{\sf{\blue{5p = - 30 +6q}}}$

$\implies{\sf{\blue{p = \frac{ - 30 + 6q}{5} }}}$

${\sf{\underline{\red{Now \:put \: the \: value \: of \: p \: in \: equation (2)}}}}$

$\implies{\sf{\blue{5( \frac{ - 30 + 6q}{5} )+ 4q = 20}}}$

$\implies{\sf{\blue{- 150 + 30q + 20q = 20 \times 5}}}$

$\implies{\sf{\blue{50q = 100 + 150}}}$

$\implies{\sf{\blue{q = \frac{250}{50}}}}$

$\implies{\sf{\blue{q =5}}}$

${\sf{\underline{\red{Now \: put \: the \: value \: of \: q \: in \: (3)}}}}$

$\implies{\sf{\blue{p= \frac{ - 30 + 6(5)}{50}}}}$

$\implies{\sf{\blue{q = \frac{ - 30 + 30}{5}}}}$

$\implies{\sf{\blue{p = 0}}}$

${\sf{\underline{\red{hence \: the \: value \: of \:p = 0 \: and \: q = 5 }}}}$