Question

Solve the following system of linear equations.

8v - 3u = 5uv
6v - 5u = - 2uv

Answer 1

$\bf\huge\boxed{\boxed{\boxed{\:Content\:Quality}}}$

Divide both sides by uv:

$\bf\huge\frac{8}{u} - \frac{3}{v} =5$

$\bf\huge\frac{6}{u} - \frac{5}{v} =-2$

Take  $\bf\huge\frac{1}{u}$ = x and  $\bf\huge\frac{1}{v}$ = y

8x - 3y = 5.. (i)

6x - 5y = -2.. (ii)

Multiplying (i) by 5 and (ii) by 3 we get

40x - 15y =25..(iii) and 18x - 15y = -6.. (iv)

Subtract (iv) from (iii),

12x = 31

x =  $\bf\huge\frac{31}{12}$

Put x =  $\bf\huge\frac{31}{12}$ in (i)

$\bf\huge\frac{62}{3}$ - 3y = 5

Y = $\bf\huge\frac{47}{9}$

U = $\bf\huge\frac{1}{x}$

Hence u = $\bf\huge\frac{21}{31}$

V = $\bf\huge\frac{1}{y}$

Hence v = $\bf\huge\frac{9}{47}$

$\bf\huge\boxed{\boxed{\boxed{\:Radhe\:Radhe}}}$

Answer 2

$\huge \bf{ \red{hey}}$

$\huge{ \mathfrak{ \pink{here \: is \: answer}}}$

Divide both sides by uv:

$\bf\huge\frac{8}{u} - \frac{3}{v} =5$

$\bf\huge\frac{6}{u} - \frac{5}{v} =-2$

$Take  \bf\huge\frac{1}{u} = x and  \bf\huge\frac{1}{v}$

8x - 3y = 5.. (i)

6x - 5y = -2.. (ii)

Multiplying (i) by 5 and (ii) by 3 we get

40x - 15y =25..(iii) and 18x - 15y = -6.. (iv)

Subtract (iv) from (iii),

12x = 31

$x=\bf\huge\frac{31}{12}$

Put x = $\bf\huge\frac{31}{12}in (i)$

$\bf\huge\frac{62}{3}y=5$

$Y=\bf\huge\frac{47}{9}$

$U=\bf\huge\frac{1}{x}$

Hence u $=\bf\huge\frac{21}{31}$

$V=\bf\huge\frac{1}{y}$

Hence v $=\bf\huge\frac{9}{47}$

$\huge \boxed{ \boxed{ \orange{hope \: it \: helps}}}$

$\huge{\purple{thanks}}$