Question

2u+v=7/3 uv , u+3v =11/3 uv. solve it please​

Answer 1

$\huge\underline{\overline{\mid\star{\mathfrak{\red{♦Solution ♦:—}}\star\mid}}}$

Given ,

$2u+v= \frac{7}{3} uv$

$\implies \: \: \large{ \frac{6u}{uv} + \frac{3v}{uv} = 7}$

$\implies \: \large{\frac{6}{v } + \frac{3}{u}} = 7 - - - - - (1)$

And,

$u+3v = \frac{11}{3} uv$

$\implies \: \frac{3u}{uv} + \frac{9v}{uv} = 11$

$\implies \: \large{\frac{3}{v} + \frac{9}{u} = 11} \: - - - - - - (2)$

Let,

$\large{ \bold{\frac{1}{u} \implies \: x}}$

$\large{ \bold{ \frac{1}{v} \implies \: y}}$

So,

( 1 ) → 6y + 3x = 7

→ 3x + 6y = 7 -------(3)

( 2 ) →3y + 9x = 11

→ 9x + 3y = 11 -------(4)

$\bold{ \mathtt{ \bold{ \underline{We \: \: will \: \: solve \: \: it \: \: by \: \: Substituting \: \: Method}}}}$

$\large{ \mathcal{Now,}}$

From eqn (3),

${ \boxed{ \bold {x \: = \frac{7 - 6y}{3}}}} \: \: - - - (5)$

Putting the value of x in eqn(4),

$\bold{9 \times \frac{7 - 6y}{3} + 3y = 11}$

$\implies \: 3(7 - 6y) + 3y = 11$

$\implies21 - 18y + 3y = 11$

$\implies \: - 15y = - 10$

$\implies \boxed{\mathtt{\bold{\: y \: = \frac{10}{15} = \frac{2}{3} }}}$

Again, putting the value of y in eqn (5),

$x \: = \frac{7 - 6 \times \frac{2}{3} }{3}$

$\implies \: x \: = \frac{7 - 4}{3}$

$\implies \: x \: = \frac{3}{3}$

$\implies \large{ \boxed { \mathtt{\bold{ x \: = 1}}}}$

Now,

$x \: = 1$

$\implies \: \frac{1}{u} = 1$

$y = \frac{2}{3}$

$\implies \: \frac{1}{v} = \frac{2}{3}$

$\implies \: v \: = \frac{3}{2}$

$\Large{\colorbox{yellow}{\underline{\underline{♠Answer♠:—\:\: u =1\:\:and\:\:v=\:\:3/2 }}}}$