Question

please help me in solving this

Answer 1

Heya !!!

(44/ X + Y) + (30 / X - Y) = 10 ---------(1)

And,

(55 / X + Y) + (40 / X - Y)= 13 ------(2)

Let 1/ X + Y = U and 1/X - Y = V and put this value in equation (1) and (2).

(44/ X + Y) + (30 / X - Y) = 10

44U + 30V = 10 --------(3)

And,

(55/X + Y)+ (40/ X - Y) = 13

55U + 40V = 13 -------(4)

From equation (3) we get,

44U + 30V = 10

44U = ( 10 - 30V )

U = ( 10 - 30V)/44 -------(5)

Putting the value of U in equation (4)

55U + 40V = 13

55 × ( 10 - 30V)/44 + 40V = 13

550 - 1650V/44 + 40V = 13

550 - 1650V + 1760V = 44 × 13

110V + 550 = 572

110V = 572 - 550

110V = 22

V = 22/110 = 2/10 = 1/5

Putting the value of V in equation (5)

U = ( 10 - 30V)/44 = 10 - 30 × 1/5 / 44

U = 10-6/44 = 4/44 = 1/11

-------------------------------

1/X + Y = U

1/ X + Y = 1/11

X + Y = 11 ---------(1)

And,

1/ X - Y = V

1/ X - Y = 1/5

X - Y = 5 ----(2)

From equation (1) we get,

X + Y = 11

X = ( 11 - Y ) ------(3)

Putting the value of X in equation (2)

X - Y = 5

11 - Y - Y = 5

-2Y = 5 - 11

-2Y = -6

Y = 6/2 = 3

Putting the value of Y in equation (3)

X = ( 11 - Y ) = ( 11 - 3 ) = 8

Hence,

X = 8 and Y = 3

★ HOPE IT WILL HELP YOU ★