Question

Solve:$2(3u-v)=5uv;2(u+3v)=5uv$.

Answer 1

$2(3u-v)=5uv$ ....$\left(1\right)$

$2(u+3v)=5uv$ ....$\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$ we get

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

$\Rightarrow 3u-v=u+3v$

$\Rightarrow 3u-u=3v+v$

$\Rightarrow 2u=4v$

$\Rightarrow u=2v$

Substitute $u=2v$ in $\left(1\right)$ we get

$2(3\times 2v-v)=5\times 2v\times v$

$\Rightarrow 6v-v=5\times v^2$

$\Rightarrow 5v=5\times v^2$

$\Rightarrow v=v^2$

$\Rightarrow v^2-v=0$

$\Rightarrow v(v-1)=0$

$\Rightarrow v=0,v=1$

Put $v=0$ in $u=2v\Rightarrow u=0$

$\therefore u=0,v=0u=2,v=1$