Question

Solve for x and y:
22/x+y+54/x-y=5
55/x+y+45/x-y=14
Please solve ......it is urgent

Answer 1

heya...

your answer is in attachment

Answer 2

Given : (22/x + y) + (54/x - y) = 5    ------ (1)

Given : (55/x + y) + (45/x - y) = 14   ------- (2)

Let 1/x + y = a and 1/x - y = b.

On solving (1) * 5 & (2) * 2, we get

⇒ 110a + 270b = 25

⇒ 110a + 90b = 28

   -------------------------

               -180b = 3

                     b = -3/180

                     b = -1/60

Then, 1/x - y = -1/60

           x - y = -60.     ------- (3)

Now,

Substitute b = -1/60 in (1), we get

⇒ 110a + 270b = 25

⇒ 110a + 270(-1/60) = 25

⇒ 110a - 270/60 = 25

⇒ 110a = 25 + (270/60)

⇒ 110 * 60a = 1770

⇒ a = 1770/6600

⇒ a = 59/220.

Then, 1/x + y = 59/220

          x + y = 220/59.     -------- (4)

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

⇒ x - y = -60

⇒ x + y = 220/59

   --------------------

   2x = -60 + (220/59)

      x = -1660/59.

Substitute x = -1660/59 in (3), we get

⇒ x - y = -60

⇒ (-1660/59) - y = -60

⇒ (-1660/59) + 60 = y

⇒ y = 1880/59

Therefore, the value of x = -1660/59 and y = 1880/59.

Hope this helps!