Question

If 1/X + 2 / Y = 4 and 3 /Y- 1 /X= 11 then value of x and y is​

Answer 1

$x=-\dfrac{1}{2},y=\dfrac{1}{3}$

Given data:

The equations $\dfrac{1}{x}+\dfrac{2}{y}=4$ and $\dfrac{3}{y}-\dfrac{1}{x}=11$

To find:

The value of x and y

Step-by-step explanation:

The given equations are

$\dfrac{1}{x}+\dfrac{2}{y}=4$ ... ... (1)

$\dfrac{3}{y}-\dfrac{1}{x}=11$ ... ... (2)

Adding (1) and (2), we get

$\dfrac{1}{x}+\dfrac{2}{y}+\dfrac{3}{y}-\dfrac{1}{x}=4+11$

$\Rightarrow \dfrac{1}{x}-\dfrac{1}{x}+\dfrac{2}{y}+\dfrac{3}{y}=15$

$\Rightarrow 0+\dfrac{5}{y}=15$

$\Rightarrow \dfrac{5}{y}=15$

$\Rightarrow \dfrac{y}{5}=\dfrac{1}{15}$

$\Rightarrow y=\dfrac{5}{15}$

$\Rightarrow \boxed{y=\dfrac{1}{3}}$

Putting $y=\dfrac{1}{3}$ in (1), we get

$\dfrac{1}{x}+\dfrac{2}{\dfrac{1}{3}}=4$

$\Rightarrow \dfrac{1}{x}+6=4$

$\Rightarrow \dfrac{1}{x}=-2$

$\Rightarrow \boxed{x=-\dfrac{1}{2}}$

Thus the required solution is

$x=-\dfrac{1}{2},y=\dfrac{1}{3}$

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