Question

Solve:
$x+y=7xy$
$2x-3y=-xy$

• A. $x=\frac{1}{8}$ and $y=\frac{1}{4}$
• B. $x=\frac{1}{7}$ and $y=\frac{1}{4}$
• C. $x=\frac{1}{2}$ and $y=\frac{1}{4}$
• D. $x=\frac{1}{3}$ and $y=\frac{1}{4}$

Answer 1

The correct option is D $x=\frac{1}{3}$ and $y=\frac{1}{4}$

Given equations are

$x+y=7xy$ ....(1)

and $2x-3y=-xy$ ....(2)

Multiply equation (1) by $3$, we get

$3x+3y=21xy$ ....(3)

Add equations (2) and (3),

$5x=20xy$

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

Put this value in equation (1), we get

$x+\frac{1}{4}=7x\times \frac{1}{4}$

$\Rightarrow x-\frac{7x}{4}=-\frac{1}{4}$

$\Rightarrow \frac{3x}{4}=\frac{1}{4}$

$\Rightarrow x=\frac{1}{3}$

Therefore, solution is $x=\frac{1}{3},y=\frac{1}{4}$.