\[\dot{x}=x+2y\]
\[\dot{y}=y\]
Phase space diagrams illustrate the direction of the velocity field, in this example
\[\begin{pmatrix}\dot{x}\\ \dot{y}\end{pmatrix}=\begin{pmatrix}x+2y\\y\end{pmatrix}\]
.At each point
\[(x,y)\]
draw the vector \[\begin{pmatrix}x+2y\\y\end{pmatrix}\]
.