Question

The solution of the system of equations $\frac{2x+5y}{xy}=6$ and $\frac{4x-5y}{xy}+3=0$ (where $x\ne 0,y\ne 0$), respectively is ___________.

• A. $1,2$
• B. $0,0$
• C. $-1,2$
• D. $1,-2$

Answer 1

The correct option is A $1,2$

Equation $1:\frac{2x+5y}{xy}=6$

$\Rightarrow 2x+5y=6xy$ ........ $\left(1\right)$

Equation $2:\frac{4x-5y}{xy}+3=0$

$\Rightarrow 4x-5y=-3xy$ ........ $\left(2\right)$

Adding both the equations, we get $6x=3xy$

$\therefore y=2$

Substituting value of $y$ in $\left(1\right)$ we get

$2x+10=12x$

$\therefore x=1$