Question

Solve :
5/(x+y)−2/(x−y)+1=0,15/(x+y)+7/(x−y)−10=0

Answer 1

5/(x+y)−2/(x−y)=−1 .................. (1)

15/(x+y)+7/(x−y)=10 ................. (2)

Let 1x+y=u and 1x−y=v

Then equation (1) and (2) becomes,

5u−2v=−1 ................. (3)

15u+7v=10 ...............(4)

Multiply equation (3) with 3,

15u−6v=−3 ................. (5)

Now subtract the above result from equation (4),

7v+6v=10+3

13v=13

v=1

⇒x−y=1 ................... (6)

From equation (3),

5u=−1+2v

5u=−1+2

5u=1

u=1/5

⇒x+y=5 ................... (7)

Adding (6) and (7) , we get,

2x=6

x=3

From equation (7),

y=5−x

y=5−3

y=2