Question

3/x+1/y=8;4/x-2/y=2

Answer 1

Let $\frac{1}{x}$ be m and $\frac{1}{y}$ be n

The equations, then, will be :

3m + n = 8 ...(i)

4m - 2n = 2 ...(ii)

Now let us solve this by substitution method:

Equation (i)

$3m + n = 8 \\ \bf n = 8 - 3m \: \: \: \: \: \: \: \: \: \: \: ...(iii)$

Substituting the value of n in equation (ii) we get:

4m - 2(8 + 3m) = 2

4m - 16 - 6m = 2

-2m = 2 + 16

-2m = 18

-m = 9

m = -9

Putting the value of m in equation (ii)

4(-9) - 2n = 2

-36 - 2n = 2

-2n = 2 + 36

-2n = 38

-n = 19

n = - 19

Now,

We assumed $\frac{1}{x}$ as m:

$\frac{1}{x} = m \\ \\ \frac{1}{x} = - 9 \\ \\ x = - \frac{1}{9}$

and $\frac{1}{y}$ as n

So,

$\frac{1}{y} = n \\ \\ \frac{1}{y} = - 19 \\ \\ y = - \frac{1}{19}$