Question

find x and y.
solve the equation...​

Answer 1

Answer:

$x = \frac{5}{2}$

$y =\frac{1}{2}$

Step-by-step explanation:

Given :

To find the value of x & y if,

$\frac{3}{x+y} + \frac{2}{x-y} = 2 ..(i)$

&

$\frac{9}{x+y} - \frac{4}{x-y} = 1 ..(ii)$

Solution :

Adding both the equations,

=>(i) × 2 + (ii)

=>$(\frac{3}{x+y} + \frac{2}{x-y})(2) + (\frac{9}{x+y} - \frac{4}{x-y}) = 2(2) + 1$

=>$\frac{6}{x+y} + \frac{4}{x-y} + (\frac{9}{x+y} - \frac{4}{x-y}) = 5$

=>$\frac{15}{x+y} = 5$

=>$\frac{x + y}{15} =\frac{1}{5}$

=>$x + y =\frac{15}{5}$

=>$x + y =3 ..(iii)$

$By substituting value of (iii) in (i),We get,$

$\frac{3}{x+y} + \frac{2}{x-y} = 2$

$\frac{3}{3} + \frac{2}{x-y} = 2$

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

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

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

$x-y = 2 ...(iv)By adding (iii) & (iv),We get, (iii) + (iv) ⇒ (x + y) + (x - y) = 3 + 22x= 5$

$x = \frac{5}{2}$

$By subtracting (iv) from (iii),We get,(iii) - (iv) ⇒ (x + y) - (x - y) = 3 - 2 2y = 1$

$y =\frac{1}{2}$

$x = \frac{5}{2}$

$y =\frac{1}{2}$

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