Question

solve the equation by reducing to a pair of linear equations 10/x+y + 2/x-y=4 and 15/x+y - 5/x-y=-2

Answer 1

Answer :

x = 3 , y = 2

Solution :

Here ,

The given equations are ;

10/(x + y) + 2/(x - y) = 4

15/(x + y) - 5/(x - y) = -2

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

10a + 2b = 4 --------(1)

15a - 5b = -2 -------(2)

Now ,

Multiplying eq-(1) by 5 , we get ;

=> 5(10a + 2b) = 5•4

=> 50a + 10b = 20 ------(3)

Also ,

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

=> 2(15a - 5b) = 2•(-2)

=> 30a - 10b = -4 ---------(4)

Now ,

Adding eq-(3) and (4) , we get ;

=> 50a + 10b + 30a - 10b = 20 + (-4)

=> 80a = 16

=> a = 16/80

=> a = 1/5

=> 1/(x + y) = 1/5

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

Now ,

Putting a = 1/5 in eq-(1) , we get ;

=> 10a + 2b = 4

=> 10•(1/5) + 2b = 4

=> 2 + 2b = 4

=> 2b = 4 - 2

=> 2b = 2

=> b = 2/2

=> b = 1

=> 1/(x - y) = 1

=> x - y = 1 ---------(6)

Now ,

Adding eq-(5) and (6) , we get ;

=> x + y + x - y = 5 + 1

=> 2x = 6

=> x = 6/2

=> x = 3

Now ,

Putting x = 3 in eq-(5) , we get ;

=> x + y = 5

=> 3 + y = 5

=> y = 5 - 3

=> y = 2

Hence ,

x = 3 , y = 2