Solve the following system of equations:
$\frac{15}{u}\ +\ \frac{2}{v}\ =\ 17$
$\frac{1}{u}\ +\ \frac{1}{v}\ =\ \frac{36}{5}$

Given:

The given system of equations is:

$\frac{15}{u}\ +\ \frac{2}{v}\ =\ 17$

$\frac{1}{u}\ +\ \frac{1}{v}\ =\ \frac{36}{5}$

To do:

We have to solve the given system of equations.

Solution:

Let $\frac{1}{u}=x$ and $\frac{1}{v}=y$

This implies,

The given system of equations can be written as,

$\frac{15}{u}\ +\ \frac{2}{v}\ =\ 17$

$15x+2y=17$-----(i)

$\frac{1}{u}\ +\ \frac{1}{v}\ =\ \frac{36}{5}$

$x+y=\frac{36}{5}$

$5x+5y=36$

$5x=36-5y$

$x=\frac{36-5y}{5}$

Substitute $x=\frac{36-5y}{5}$ in equation (i), we get,

$15(\frac{36-5y}{5})+2y=17$

$3(36-5y)+2y=17$ 

$108-15y+2y=17$ 

$-13y=17-108$

$-13y=-91$ 

$y=\frac{-91}{-13}$

$y=7$

This implies,

$x=\frac{36-5(7)}{5}$

$x=\frac{36-35}{5}$

$x=\frac{1}{5}$

$u=\frac{1}{x}=\frac{1}{\frac{1}{5}}=5$

$v=\frac{1}{y}=\frac{1}{7}$ 

Therefore, the solution of the given system of equations is $u=5$ and $v=\frac{1}{7}$. 

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Updated on: 10-Oct-2022

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