Question

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

• A. $x=-\frac{7}{2}$ and $y=-\frac{2}{3}$
• B. $x=\frac{6}{7}$ and $y=-\frac{2}{5}$
• C. $x=\frac{4}{3}$ and $y=-\frac{4}{3}$
• D. $x=\frac{1}{3}$ and $y=\frac{1}{4}$

Answer 1

Answer: (D)

$x=\frac{1}{3}$ and $y=\frac{1}{4}$

The given equations are:

$x+y=7xy.........\left(1\right)$

$2x-3y=-xy.........\left(2\right)$

Multiply the equation 1 by $2$.Then we get:

$2x+2y=14xy.........\left(3\right)$

Subtract equation 2 from equation 3 to eliminate $x$, because the coefficients of $x$ are same. So, we get

$(2x-2x)+(2y+3y)=14xy+xy$

i.e. $5y=15xy$

i.e. $5=15x$

i.e. $x=\frac{1}{3}$

Substituting this value of $x$ in the equation 1, we get

$\frac{1}{3}+y=\frac{7}{3}y\Rightarrow \frac{1}{3}=\frac{7}{3}y-y\Rightarrow \frac{1}{3}=\frac{4}{3}y\Rightarrow 4y=1\Rightarrow y=\frac{1}{4}$

Hence, the solution of the equations is $x=\frac{1}{3},y=\frac{1}{4}$.