Question
Solve :$x + y = 2xy,x - y = 6xy$
✓
Answer
$x+y=2 x y\ldots . .(1)$
$x-y=6 x y\ldots . . .(2)$
Adding equation $( 1 )$ and $( 2 )$
$x+y=2 x y + x-y=6 x y- 2 x=8 x y$
$ 2=8 y$
$ y=\frac{1}{4}$
From $(1)$
$x+\frac{1}{4}=2 \times\left(\frac{1}{4}\right)$
$ \frac{1}{2} x=-\frac{1}{4}$
$ x=-\frac{1}{2}$
$x-y=6 x y\ldots . . .(2)$
Adding equation $( 1 )$ and $( 2 )$
$x+y=2 x y + x-y=6 x y- 2 x=8 x y$
$ 2=8 y$
$ y=\frac{1}{4}$
From $(1)$
$x+\frac{1}{4}=2 \times\left(\frac{1}{4}\right)$
$ \frac{1}{2} x=-\frac{1}{4}$
$ x=-\frac{1}{2}$
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