Solve 15/x+2/y=17 and 1/x+1/y=36/5
$\frac{15}{{\mathrm{x}}} + \frac{2}{{\mathrm{y}}} = 17$ —(i)
$\frac{1}{{\mathrm{x}}} + \frac{1}{{\mathrm{y}}} = \frac{36}{5}$ —-(ii)
Let, $\frac{1}{{\mathrm{x}}}$ = u and $\frac{1}{{\mathrm{y}}}$ =v
Then equations (i) and (ii) become,
15u+2v=17 —(iii)
u+v=$\frac{36}{5}$ —(iv)
Multiplying equation (iv) by 2 we get,
2u+2v=$\frac{72}{5}$ —-(v)
Now Subtracting Equations (v) from (iii) we get,
15u+2v – 2u-2v = 17-$\frac{72}{5}$
13u=$\frac{85 – 72}{5}$
13u=$\frac{13}{5}$
u= $\frac{1}{5}$
From Equation (iii) we get,
$15\left(\frac{1}{5}\right) + 2{\mathrm{v}} = 17$
$\Rightarrow 3 + 2{\mathrm{v}} = 17$
$\Rightarrow 2{\mathrm{v}} = 17 – 3$
$\Rightarrow 2{\mathrm{v}} = 14$
$\Rightarrow {\mathrm{v}} = \frac{14}{2}$
$\Rightarrow {\mathrm{v}} = 7$
$\therefore {\mathrm{x}} = \frac{1}{{\mathrm{u}}} = \frac{1}{\frac{1}{5}} = 1 \div \frac{1}{5} = 1 \times 5 = 5 $
and $\ y = \frac{1}{v} = \frac{1}{7}$
∴ Required Solutions are , x =5 and y = $\frac{1}{7}$