Question:
Solve the following systems of equations:
$\frac{15}{u}+\frac{2}{\nu}=17$
$\frac{1}{u}+\frac{1}{\nu}=\frac{36}{5}$
Solution:
The given equations are:
$\frac{15}{u}+\frac{2}{v}=17$
$\frac{1}{u}+\frac{1}{v}=\frac{36}{5} \ldots(i i)$
Multiply equation (ii) by 2 and subtract (ii) from (i), we get
$\frac{15}{u}+\frac{2}{v}=17$
Put the value of $u$ in equation $(i)$, we get
$\frac{15}{5}+\frac{2}{v}=17$
$\Rightarrow \frac{2}{v}=14$
$\Rightarrow v=\frac{1}{7}$
Hence the value of $u=5$ and $v=\frac{1}{7}$.