Question

find the solution of x-y = 0.9 and 11/(x+y) = 2

Answer 1

The answer is given below :

Given that,

x - y = 0.9

⇒ x - y = 9/10 .....(i)

and

11/(x + y) = 2

⇒ (x + y)/11 = 1/2

⇒ x + y = 11/2 .....(ii)

Now, adding the two equations (i) and (ii), we get

x - y + x + y = 9/10 + 11/2

⇒ 2x = (9 + 55)/10, since lcm of 10 and 2 is 10

⇒ 2x = 64/10

⇒ x = 64/20

⇒ x = 16/5

Now, putting x = 16/5 in (i) no equation, we get

16/5 - y = 9/10

⇒ y = 16/5 - 9/10

⇒ y = (32 - 9)/10, since lcm of 5 and 10 is 10

⇒ y = 23/10

So, the required solution is
x = 16/5 and y = 23/10.

VERIFICATION :

Putting x = 16/5, y = 23/10 in LHS of (i), we get

LHS = 16/5 - 23/10

= (32 - 23)/10, since lcm of 5 and 10 is 10

= 9/10 = RHS

Again, putting x = 16/5 and y = 23/10 in LHS of (ii), we get

LHS = 16/5 + 23/10

= (32 + 23)/10, since lcm of 5 and 10 is 10

= 55/10

= 11/2 = RHS

Thus, verified.

Thank you for your question.

Answer 2

=> x - y = 0.9

=> x - y = 9/10 ------1equation
-------------------------

=> 11/(x+y) = 2

=> 11/2 = (x+y)

=> 11/2 = x+y -----2equation

Adding both equations,

x -y = 9/10
x +y = 11/2
__________
2x= 9/10 + 11/2
____________

=> 2x = (9+55)/10

=> 2x = 64/10

=> x= 64/(10×2)

=> x=32/10

Putting the value of x in 1equation,

=> x - y= 9/10

=> 32/10 -y = 9/10

=> 32/10 -9/10 = y

=> (32-9)/10 = y

=> 23/10 = y

_________________

x =32/10
x = 16/5

y =23/10

I hope this will help you

-by ABHAY