Question

Solve for X and Y.

$\frac{15}{x + y} - \frac{2}{x - y} = 1$

$\frac{15}{x + y} + \frac{7}{x - y} = 10$

(x+y is not equal to 0)
(x-y is not equal to 0)​

Answer 1

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$\bf{ \purple{step \: by \: step \: explanation}}$



$\frac{15}{x + y} - \frac{2}{x - y} = 1......(1) \\ \\ \frac{15}{x + y} + \frac{7}{x - y} = 10.....(2)$


Substrate in equation (1) and (2) , we get

$\sf \cancel{ \frac{15}{x + y}} - \frac{2}{x - y} = 1. \\ \\ \sf \cancel\frac{15}{x + y} + \frac{7}{x - y} = 10. \\ \\ - \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: = - \\ ...................................... \\ \\ \sf \implies - \frac{2}{x - y} - \frac{7}{x - y} = - 9. \\ \\ \sf \implies \frac{ \cancel{ - 9}}{x - y} = \cancel{ - 9}. \\ \\ \sf \implies x - y = 1................(3).$

put the value of x - y in equation ( 1 )

$\sf{ \frac{15}{x + y} - \frac{2}{1} = 1.}$


$\sf{ \frac{ \cancel{15}}{x + y} = \cancel{3}}$
$\sf{ \implies \: x + y = 5....(4)}$


From equation (3) & (4)



x + y = 5
x - y = 1
_______

2y= 4

y= 4/2

y = 2 .

put the value of y in equation (3)

x - y = 1

x - 2 = 1

x = 1+2

x = 3


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Answer 2

Solution:-

Given Equation:-

$(1). \frac{15}{x + y} - \frac{2}{x - y} = 1$

& Second :-

$(2). \frac{15}{x + y} + \frac{7}{x - y} = 10$

Taking a = 1/(x+y) & b= 1/(x-y).

Now, The Equations are :-

15a - 2b = 1 _________(1).

& 15a + 7b = 10 ______(2).

By Elimination Method,

- 9b = -9

=> b = 1.

Putting b=1 in equation (1). we get,

15a = 1 + 2

=> 15a = 3

=> a = 1/5.

Now,

As per our Assumptions;

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

=> x + y = 5 ________(3).

& b = 1 = 1/(x-y)

=> x -y = 1._________(4).

Again Applying Elimination Method, we get

2x = 6

=> x = 3

& Putting x = 3 in eq (4).

=> 3 - y = 1

=> y = 2.