Question

solve for x and y
(10/x+y)+(2/x-y)=4
(15/x+y)-(9/x-y)=-2

Answer 1

Answer:

$x=\frac{21}{8}$

$y=\frac{9}{8}$

Step-by-step explanation:

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Take $\frac{1}{x+y}=A$

Take $\frac{1}{x-y} =B$

Then, it is system equation of A, B

Method :

$10A+2B=4$ ...... eq.1

$15A-9B=-2$ ...... eq.2

LCM of 10, 15 is 30

Multiply 3 and 2 on both equations

$30A+6B=12$

$30A-18B=-4$

We have $24B=16$, therefore solution is $\frac{2}{3}$.

Therefore $\frac{1}{x-y} =\frac{2}{3}$, it means $x-y=\frac{3}{2}$.

Substitute it in eq.2

$15A-6=-2$

We have $15A=4$, therefore solution is $\frac{4}{15}$.

Therefore $\frac{1}{x+y} =\frac{4}{15}$, it means $x+y=\frac{15}{4}$.

System equation

$x+y=\frac{15}{4}$, $x-y=\frac{3}{2}$

$2x=\frac{21}{4}$, therefore $x=\frac{21}{8}$

$2y=\frac{9}{4}$, therefore $y=\frac{9}{8}$