Question

Solve :
$x+y=2xy$
$x-y=6xy$

• A. $x=-\frac{1}{2}$ and $y=\frac{1}{7}$
• B. $x=-\frac{1}{2}$ and $y=\frac{1}{4}$
• C. $x=-\frac{1}{2}$ and $y=\frac{1}{2}$
• D. $x=-\frac{1}{2}$ and $y=\frac{1}{5}$

Answer 1

The correct option is B $x=-\frac{1}{2}$ and $y=\frac{1}{4}$

Let $x+y=2xy$ --- $\left(1\right)$
$x-y=6xy$ ----- $\left(2\right)$
Adding equations $\left(1\right)$ and $\left(2\right)$, we get

$2x=8xy$

$\Rightarrow y=\frac{1}{4}$

Substituting $y=\frac{1}{4}$ in the equation $\left(1\right)$, we get

$x+\frac{1}{4}=2\left(x\right)\left(\frac{1}{4}\right)$

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