Solve the following system of equations:
$2(3u-v)=5uv$
$2(u+3v)=5uv$

Given:

The given system of equations is:

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

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

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

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

$6u-2v=5uv$

$3(6u-2v)=3(5uv)$   (Multiplying by 3 on both sides)

$18u-6v=15uv$---(i)

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

$2u+6v=5uv$---(ii)

Adding equations (i) and (ii), we get,

$18u-6v+2u+6v=15uv+5uv$

$20u=20uv$

$\frac{uv}{u}=\frac{20}{20}$

$v=1$

Using $v=1$ in equation (i), we get,

$18u-6(1)=15u(1)$

$18u-6=15u$

$18u-15u=6$

$3u=6$

$u=\frac{6}{3}$

$u=2$

Therefore, the solution of the given system of equations is $u=2$ and $v=1$.  

Tutorialspoint

Updated on: 10-Oct-2022

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