Solve for 'u' and 'v', $2 (3 u - v) = 5 u v$ ; and $2 (u + 3 v) = 5$ uv.

Open in App

Solution

$\begin{matrix} 2 (3 x - v) = 5 u v \Rightarrow 2 (\frac{3 x}{u v} - \frac{v}{u v}) = \frac{5 u v}{u v} 2 (\frac{3}{v} - \frac{1}{u}) = 5 \to (i) a n d 2 (u + 3 v) = 5 u v \Rightarrow 2 (\frac{u}{u v} + \frac{3 v}{u v}) = \frac{5 u v}{u v} \Rightarrow 2 (\frac{1}{v} + \frac{3}{u}) = 5 \to (i i) L e t \frac{1}{v} = x, \frac{1}{u} = y f r o m e q u a t i o n (i) a n d (i i) \Rightarrow 2 (3 x - y) = 5 \Rightarrow 3 x - y = \frac{5}{2} \to (i i) a n d \Rightarrow 2 (x + 3 y) = 5 \Rightarrow x + y = \frac{5}{2} a d d i n g e q u a t i o n (i i i) a n d (i v) 3 x - y = \frac{5}{2} \times 1 x + 3 y = \frac{5}{2} \times 3 3 x - y = 5 / 2 3 x - - - + - - 9 y = \frac{15}{- 2} - 10 y = - 5, y = \frac{5}{10} = \frac{1}{2} = \frac{1}{u} u = 2 P u t t i n g = \frac{1}{2} i n e q u a t i o n (i i i) \Rightarrow 3 x \frac{- 1}{2} = \frac{5}{2} \Rightarrow 3 x = 3 x = 1 = \frac{1}{v} ∴ v = 1 a n d u = 2 A n s . \end{matrix}$

Suggest Corrections

Similar questions

2 (3 u - v) = 5 u v; 2 (u + 3 v) = 5 u v

2 (3 u - v) = 5 u v

2 (u + 3 v) = 5 u v

\neq 0

2 (3 u - v) = 5 u v 2 (u + 3 v) = 5 u v

Solve the following systems of equations:

$2 (3 u - v) = 5 u v$

$2 (u + 3 v) = 5 u v$

3 (2 u + v) = 7 u v

3 (u + 3 v) = 11 u v

Join BYJU'S Learning Program