A past exam paper I'm working on (Mathematics BSc, second-year module in differential equations, unpublished) has a question to plot the nullcline diagram of the system of ODEs, \begin{align} & \dot{x} = 2x - 2x^2 -xy, \\ & \dot{y} = 2y - 2y^2 - 3xy. \end{align} I found 4 equilibrium points, namely $(0,0),\;(0,1),\;(1,0),\;(2,-2)$. When I try to find the nullclines I get linear equations, \begin{align} & y = 2 - 2x, \\ & y = 1 - \frac{3}{2}x \end{align} but these can't intersect at all 4 of the equilibrium points. This makes me think I shouldn't be dividing through by $x$ or $y$, so as to preserve the quadratic shape, but in that case I can't see how to get the null equations in a form I know how to plot.
Could someone point out what I'm missing/doing wrong?