Question

30/x-y+28/x+y=7
21/x-y+21x+y=5

Answer 1

Steps :

30/x-y + 28/x+y = 7 ------------ (i)

21/x-y + 21/x+y = 5 ------------- (ii)

Putting the value of 1/x-y = u and 1/x+y = v

Then it becomes

30u + 28v = 7 ---------- (iii)

21u + 21v = 5 ----------- (iv)

Multiplying equation (iii) by 21 and (iv) by 30

630u + 588v = 147 --------- (v)

630u + 630v = 150 -------- (vi)

Subtracting equation (v) from (vi)

(630u + 630v) - (630u + 588v) = 150 -147

630u + 630v - 630u - 588v = 3

42v = 3

v = 3/42

v = 1/14

Substituting the value of v in equation (iii)

30u + 28 x 1/14 = 7

30u + 2 = 7

30u = 7 - 2

30u = 5

u = 5/30

u= 1/6

Now,

v = 1/14

1/x+y = 1/14

x+y = 14 --------- (vii)

And

u = 1/6

1/x-y = 1/6

x-y = 6 --------- (viii)

Adding equation (vii) and (Viii)

(x+y) + (x-y) = 16+4

x+y+x-y = 20

2x = 20

x = 20/2

x = 10

Substituting the value of x in equation (vii)

x+y = 16

10 + y = 16

y = 16-10

y = 6

Therefore,

x = 10

y = 6