Question

3/x+y + 2/x-y = 2 And 9/x+y - 4/x-y = 1 Solve For X And Y By Elimination Method​

Answer 1

Answer :

x = 5/2 , y = 1/2

Solution :

Here ,

The given equations are ;

3/(x + y) + 2/(x - y) = 2

9/(x + y) - 4/(x - y) = 1

Putting 1/(x + y) = a and 1/(x - y) = b , the given equations will be reduced to ;

3a + 2b = 2 --------(1)

9a - 4b = 1 ---------(2)

Now ,

Multiplying eq-(1) by 2 , we get ;

=> 2×(3a + 2b) = 2×2

=> 6a + 4b = 4 -------(3)

Now ,

Adding eq-(2) and (3) , we get ;

=> 9a - 4b + 6a + 4b = 1 + 4

=> 15a = 5

=> a = 5/15

=> a = 1/3

=> 1/(x + y) = 1/3

=> x + y = 3 ----------(4)

Now ,

Putting a = 1/3 in eq-(1) , we get ;

=> 3a + 2b = 2

=> 3×(1/3) + 2b = 2

=> 1 + 2b = 2

=> 2b = 2 - 1

=> 2b = 1

=> b = 1/2

=> 1/(x - y) = 1/2

=> x - y = 2 ---------(5)

Now ,

Adding eq-(4) and (5) , we get ;

=> x + y + x - y = 3 + 2

=> 2x = 5

=> x = 5/2

Now ,

Putting x = 5/2 in eq-(4) , we get ;

=> x + y = 3

=> 5/2 + y = 3

=> y = 3 - 5/2

=> y = (6 - 5)/2

=> y = 1/2

Hence , x = 5/2 , y = 1/2 .