Solve 15/x+2/y=17 and 1/x+1/y=36/5

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 = $\frac{1}{7}$

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