Question

Solve

x + y = 2xy

x - y = 6xy

• A. $x=\frac{-1}{2}andy=\frac{1}{4}$
• B. $x=\frac{1}{2}andy=\frac{-1}{4}$
• C. $x=\frac{1}{4}andy=\frac{-1}{4}$
• D. $x=\frac{-1}{2}andy=\frac{-1}{2}$

Answer 1

The correct option is A

$x=\frac{-1}{2}andy=\frac{1}{4}$

Given equations : $x+y=2xyandx-y=6xy$

Divide both equations by xy

$\frac{1}{y}+\frac{1}{x}=2$ and $\frac{1}{y}-\frac{1}{x}=6$

Adding the above two equations we get

$\frac{2}{y}=8$

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

Substitute value of $y$ in any of the two equations we get

$4+\frac{1}{x}=2$

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