Question

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Answer 1

Answer:

Step-by-step explanation:

{10(x-y) + 2(x+y)} /x^2-y^2 = 4

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

8x - 8y = 4(x^2-y^2)

8(x-y)=4(x^2-y^2)

2x-2y=x^2-y^2  ............(1) = (2x-2y)/x^2-y^2 = 1 ...........(3)

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

15x-15y-5x-5y = -2(x^2-y^2)

10x-10y=-2(x^2-y^2)

10(x-y)=-2(x^2-y^2)

5y-5x=x^2-y^2 .......................(2) = (5y-5x)/x^2-y^2=1 ...............(4)

dividing eq (3) by(4)

2x-2y/5y-5x=1

2x-2y=5y-5x

7x=7y

x=y

Answer 2

Answer :

x = 3 , y = 2

Solution :

The given equations are ;

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

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

Substituting 1/(x + y) = a and 1/(x - y) = b , the given equations will reduce to linear equations as follow ;

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

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

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

=> 5(10a + 2b) = 4×5

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

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

=> 10/5 + 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