Question

Find the value of (x + y) from the given set of equations:
11/x + 19/y = 79
19/x + 11/y = 71​

Answer 1

Step-by-step explanation:

Given:-

11/x + 19/y = 79

19/x + 11/y = 71

To find:-

Find the value of (x + y) from the given set of equations:

11/x + 19/y = 79

19/x + 11/y = 71

Solution:-

Given pair of given equations are :-

11/x + 19/y = 79 ----------(1)

=>11(1/x)+19(1/y)=79

Put , 1/x=a and 1/y=b then

11a+19b=79------------(2)

19/x + 11/y = 71

=>19(1/x)+11(1/y)=71

19a+11b=71-------------(3)

on adding (2)&(3) then

11a+19b=79

19a+11b=71

(+)

____________

30a+30b=150

____________

=>30(a+b)=150

=>a+b=150/30

a+b=5--------------(4)

On subtracting (1) from (2) then

19a+11b=71

11a+19b=79

(-)

___________

8a-8b=-8

_________

=>8(a-b)=-8

=>a-b=-8/8

a-b= -1 -------------(5)

now ,on adding (4) and (5)

a+b=5

a-b= -1

(+)

______

2a+0=4

______

=>2a=4

=>a=4/2

a=2 ---------(6)

On Substituting the value of a in (4) then

=>2+b=5

=>b=5-2

b=3

The value of a=2

=>1/x=2

x=1/2

The value of b=3

=>1/y=3

y=1/3

Now ,the value of x+y

=>(1/2)+(1/3)

LCM of 2 and 3=6

=>(3+2)/6

=>5/6

Hence, x+y=5/6

Answer:-

The value of (x+y) for the given problem is 5/6