Question

Solve :x+y/xy=3/2
and x-y/xy=1/2
​

Answer 1

x = 2  , y = 1 if (x + y) /xy  = 3/2 & (x - y) /xy  = 1/2    

Step-by-step explanation:

(x + y) /xy  = 3/2   Eq 1

(x - y) /xy  = 1/2    Eq 2

Eq1 / Eq 2

(x + y) /(x - y)  = 3/1

=> x + y = 3x - 3y

=> 2x = 4y

=> x = 2y

putting x = 2y  in Eq 1

(2y + y) /(2y * y)  = 3/2

=> 3y / 2y² = 3/2

=> 6y² = 6y

=> y = 1

x = 2y = 2

x = 2  , y = 1

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Answer 2

Answer:

x = 2 and y = 1

Step-by-step explanation:

Given equations,

$\frac{x+y}{xy}=\frac{3}{2}\text{ and }\frac{x-y}{xy}=\frac{1}{2}$

From first equation,

$\frac{1}{y}+\frac{1}{x}=\frac{3}{2}$  ------(X)

From second equation,

$\frac{1}{y}-\frac{1}{x}=\frac{1}{2}$ --------(Y)

Equation (X) + Equation (Y),

We get,

$\frac{2}{y}=\frac{4}{2}$

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

$\implies y = 1$

From equation (X),

$1+\frac{1}{x}=\frac{3}{2}$

$\frac{1}{x}=\frac{3-2}{2}$

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

$\implies x = 2$