Question

7/y - 2/x = 5. 8/y + 7/x = 15​

Answer 1

Question:-

Solve for x and y :-

$\bf \: \frac{7}{y} - \frac{2}{x} = 5 \: \: and \: \: \frac{8}{y} + \frac{7}{x} = 15$

Solution:-

Putting 1/x = u and 1/y = v , then equation becomes

7v - 2u = 5 ...............(i)

8v + 7u = 15 ................(ii)

Using elimination method

Multiplying (i) by 7 and (ii) by 2 we get

49v - 14u = 35 ..............(i)

16v+ 14u = 30 ..............(ii)

Adding the results, we get

49v - 14u + 16v + 14u = 30 + 35

=> 65v = 65

=> v = 1

Putting v= 1 in (ii) , we get

16v + 14u = 30

=> 16 × 1 + 14u = 30

=> 14u = 14

=> u = 1

Now

u = 1

=> 1/x = 1

=> x = 1

And

v = 1

=> 1/y = 1

=> y = 1

Answer:- x = 1 and y = 1