Solve the linear equation for x and y, x+y divides xy=2, x-y divides xy= 6
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The answer is 6,3 respectively !
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According the question,
(xy)/(x+y) = 2, and,
(xy)/(x-y) = 6,
Now , we know that xy remains constant, So let us equal two xy's,
The first equation ,
xy = 2(x+y) ...........(1),
The second equation,
xy = 6(x-y) ............(2),
Now let us equal them as they are already equal,
=> (1) = (2),
=> 6(x-y) = 2(x+y),
=> 3(x-y) = x+y,
=> 3x - 3y = x + y,
=> 2x = 4y,
=> x = 2y, Substituting this value in 1st equation,
2y² / 3y = 2,
=> 2y² = 6y, Diving y on both the sides,
=> 2y = 6,
=> y = 3,
Now, x = 2y = 2*3 = 6,
Therefore the value of x is 6 and the value of y is 3,
Hope you understand, Have a great day !
(xy)/(x+y) = 2, and,
(xy)/(x-y) = 6,
Now , we know that xy remains constant, So let us equal two xy's,
The first equation ,
xy = 2(x+y) ...........(1),
The second equation,
xy = 6(x-y) ............(2),
Now let us equal them as they are already equal,
=> (1) = (2),
=> 6(x-y) = 2(x+y),
=> 3(x-y) = x+y,
=> 3x - 3y = x + y,
=> 2x = 4y,
=> x = 2y, Substituting this value in 1st equation,
2y² / 3y = 2,
=> 2y² = 6y, Diving y on both the sides,
=> 2y = 6,
=> y = 3,
Now, x = 2y = 2*3 = 6,
Therefore the value of x is 6 and the value of y is 3,
Hope you understand, Have a great day !
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