Question

Intriguing one.

$\frac{1}{x + y} = \frac{12}{13} \\ \\ \frac{1}{x - y} = \frac{11}{13}$

Solve for x and y.

Answer 1

Answer :

Given that

1/(x + y) = 12/13

⇒ x + y = 13/12 ...(i)

1/(x - y) = 11/13

⇒ x - y = 13/11 ...(ii)

Now, adding (i) and (ii), we get

x + y + x - y = 13/12 + 13/11

⇒ 2x = (143 + 156)/132, since LCM (12, 11) = 132

⇒ 2x = 299/132

⇒ x = 299/264

From (i), we get

299/264 + y = 13/12

⇒ y = 13/12 - 299/264

⇒ y = - 13/264

Therefore, the required solution be

x = 299/264, y = - 13/264

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Answer 2

Given : 

12x + 12y = 13  ----- (1)

11x - 11y = 13   ------- (2)

On adding (1) & (2), we get

12x + 12y + 11x - 11y = 13 + 13

23x + y = 26  ----- (3)


On subtracting (1) & (2), we get

12x + 12y - 11x + 11y = 13 - 13

x + 23y = 0   ------- (4)


On solving (3) & (4) * 23, we get

23x + y = 26

23x + 529y = 0

--------------------------

          -528y = 26

               y = -26/528

               y = -13/264



Substitute y = -13/264 in (3), we get

23x + y = 26

23x + (-13/264) = 26

23x - 13/264 = 26

23x = 26 + 13/264

23x = 6877/264

x = 6877/264 * 23

x = 6877/6072

x = 299/264.



Therefore the value of x = -13/264, y = 299/264.


Hope this helps!