• # question_answer The solution of the system of equations $\frac{2x+5y}{xy}=6$ and $\frac{4x-5y}{xy}+3=0$ (where $x\ne 0,\,\,y\ne 0$), is ____. A)  1,2                             B)  0, 0                C)  $-1,\text{ }2$         D)         $1,-2$

We have, $\frac{2x+5y}{xy}=6$ or $\frac{2}{y}+\frac{5}{x}=6$   ?.(1) Also, $\frac{4x-5y}{xy}=-3$ or $\frac{4}{y}-\frac{5}{x}=-3$       ....(2) Let $\frac{1}{y}=a$  and $\frac{1}{x}=b$ So, (1) and (2) become $2a+5b=6$                               ...(3) and,  $4a-5b=-3$                      ...(4) Adding (3) and (4), we get $a=\frac{1}{2}$  and $b=1$                   [From (3)] $\therefore$   $x=1$  and $y=2$