Question

Please solve question no. 5 in class 10th The answer is x= 1/6,y= 1/4.

Answer 1

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We have

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

and

$\frac{1}{x} + \frac{1}{2y} = 8$

Solving both a little

We have

=> y - 2x = - 2xy -------(1)

and

=> 2y + x = 16xy ------(2)

Arranging (1) and (2) properly

=> 2x - y = 2xy
and
=> x + 2y = 16xy

Multiply (1) with 2

=> 4x - 2y = 4xy

For Elimination part refer to the attachment

Thus x = 1/6
and
y = 1/4

=> Answer corrected

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Answer 2

1/2x - 1/y =-1 , 1/x + 1/2y = 8
Put 1/x = a and 1/y = b

1/2x - 1/y =-1 ....(i)
1/x + 1/2y = 8 ,.......(ii)
Putting the value of 1/x = a and 1/y = b

1) a/2 - b = - 1
Taking LCM
(a -2b )/2 = -1
a - 2b = -2 ........(iii)

2) a + b/2 = 8
Taking LCM
(2a +b)/2 = 8
2a + b = 16
Multiply it with 2 so that one exponent will be equal from the two eq..

So
4a + 2b = 32.....(iv)
Now add eq (iii) and (iv)
So

a - 2b +4a + 2b = -2 + 32
5a = 30
a = 6

Putting the value of a in eq.. (iii)

a -2b = -2
Putting a = 6
6-2b = -2
-2b = -2-6
2b = 8
b = 4

a = 1/x
6 = 1/x
x = 1/6

b = 1/y
4 = 1/y

y = 1/4