Solve the following systems of equations:
Question:

Solve the following systems of equations:

$x+y=5 x y$

$3 x+2 y=13 x y$

$x \neq 0, y \neq 0$

Solution:

The given equations are:

$x+y=5 x y \quad \ldots(i)$

$3 x+2 y=13 x y \quad \ldots(i i)$

Multiply equation $(i)$ by 2 and subtract (ii) from (i), we get

Put the value of $y$ in equation $(i)$, we get

$x+\frac{1}{3}=5 x \times \frac{1}{3}$

$\Rightarrow \frac{2 x}{3}=\frac{1}{3}$

$\Rightarrow x=\frac{1}{2}$

Hence the value of $x=\frac{1}{2}$ and $y=\frac{1}{3}$