Question

Solve $x+4y=24xy$, $x+2y=21xy$.

Answer 1

$x+4y=24xy⟶\left(I\right)$

$x+2y=21xy⟶\left(II\right)$

Divide both equation by $xy$

$\frac{1}{y}+\frac{4}{x}=24⟶\left(III\right)$

$\frac{1}{y}+\frac{2}{x}=21⟶\left(IV\right)$

Subtraction $\left(IV\right)$ from $\left(III\right)$

$\frac{2}{x}=3$ $x=\frac{2}{3}$

From equation $\left(IV\right)$

So, $\frac{1}{y}+3=21$

$y=\frac{1}{18}$

$x=\frac{2}{3}$ and $y=\frac{1}{18}$