Question

$6x+3y=6xy$
$2x+4y=5xy$

Answer 1

Given $6x+3y=6xy$

$⟹\frac{6x+3y}{xy}=6⟹\frac{6}{y}+\frac{3}{x}=6\cdots \left(1\right)$

$2x+4y=5xy$

$⟹\frac{2x+4y}{xy}=5⟹\frac{2}{y}+\frac{4}{x}=5\cdots \left(2\right)$

$\left(2\right)\times 3⟹\frac{6}{y}+\frac{12}{x}=15\cdots \left(3\right)$

$\left(1\right)-\left(3\right)⟹\frac{-9}{x}=-9⟹x=1$

Put $x=1$ in $\left(1\right)$

$\frac{6}{y}+\frac{3}{1}=6⟹\frac{6}{y}=3⟹y=2$