Question

( 1/x + 1/y = 4 and 1/x - 1/y = 0 ) solve it​

Answer 1

Answer:

$\frac{1}{x} = 4 - \frac{1}{y} \\ 4 - \frac{1}{y} - \frac{1}{y} = 0 \\ 4 = \frac{2}{y} \\ y = \frac{2}{4} = \frac{1}{2}$

Answer 2

Solution:-

Equation:-

$\rm \: \frac{1}{x} + \frac{1}{y} = 4 \: \: \: \: \: \: \: \: \: ......(i)eq$

$\rm \: \frac{1}{x} - \frac{1}{y} = 0 \: \: \: \: \: \: \: \: \: .......(ii)eq$

Let

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

We get

$\rm \: u + v = 4 \: \: \: \: \: \: ....(i)eq$

$\rm \: u \: - v \: = 0 \: \: \: \: \: \: ......(ii)eq$

Now using elimination methods

Add (i)eq with (ii)eq , we get

$\rm \: u + v + u - v = 4 + 0$

$\rm \: 2u = 4$

$\rm \: u \: = 2$

Now put the value on (i ) eq

$\rm \: 2 \: + v = 4$

$\rm \: v = 2$

Now we get

$\rm \: \frac{1}{x} = 2 \: \: and \: \: \frac{1}{y} = 2$

So value is

$\boxed{ \rm \: x = \frac{1}{2} \: \: and \: \: y = \frac{1}{2} }$