Solve the system: 2x − y = 2xy and x + 2y = 16xy, given x != 0, y != 0.

Here are the solutions to the systems of equations from question 3.

a) Solve the system:

$$2x - y = 2xy \quad (1)$$ $$x + 2y = 16xy \quad (2)$$

Given $x \neq 0, y \neq 0$.

Step 1: Divide both equations by $xy$.
From (1): $\frac{2x}{xy} - \frac{y}{xy} = \frac{2xy}{xy} \implies \frac{2}{y} - \frac{1}{x} = 2 \quad (3)$
From (2): $\frac{x}{xy} + \frac{2y}{xy} = \frac{16