If $3\mathrm{x} + 6\mathrm{y} = 4\mathrm{xy},9\mathrm{x} + 8\mathrm{y} = 7\mathrm{xy}$, then $\left(\mathrm{x},\mathrm{y}\right)=$   

Given equations $3\mathrm{x}+6\mathrm{y}=4\mathrm{xy}\to \left(1\right)$
$9\mathrm{x}+8\mathrm{y}=7\mathrm{xy}\to \left(2\right)$
Option (A) (2,3)  
$\mathrm{x} = 2,\mathrm{y} = 3$ substitute in equation (1)
$3\left(2\right)+6\left(3\right)=4\times 2\times 3$
$6 + 18 = 24$
$24 = 24$ false
$\mathrm{x} = 2,\mathrm{y} = 3$ substitute in the equation (2)
$9\left(2\right)+8\left(3\right)=7\times 2\times 3$
$18 + 24 = 42$
$42 = 42$ true
$\therefore \left(2,3\right) \mathrm{is} \mathrm{solution} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{equations}$
Option (B) : $\left(3,2\right)$
$\mathrm{x} = 3,\mathrm{y} = 2$ substitute in equation (1)        
$3\left(3\right)+6\left(2\right)=4\times 3\times 2$
$9 + 12 = 24$
$21\ne 24$ false
$\left(3,2\right) \mathrm{is} \mathrm{not} \mathrm{a} \mathrm{solutions}$
Option (D) :  $\left(3,-2\right)$
$\mathrm{x} = 3,\mathrm{y} = - 2$ Substitute in equation (1)
$3\left(3\right)+6\left(-2\right)=4\times 3\times -2$
$9 - 12 = - 24$
$- 3 = - 24 \mathrm{False}$
$\left(3,-2\right) \mathrm{is} \mathrm{not} \mathrm{a} \mathrm{solution}$