For assigned exercises 8-12 in 7.1, the solutions are equations in parametric form, $x_1(t)$ and $x_2(t)$.
Each value of $t$ gives a point $(x_1(t), x_2(t))$ on the curve in the $(x_1,x_2)$-plane.
One way to sketch the graph of the solution in the $(x_1,x_2)$-plane for $t \ge0$ is to evaluate $x_1(t)$ and $x_2(t)$ at different values of $t \ge 0$, where $x_1$ is the horizontal axis and $x_2$ is the vertical axis.
Not sure if there is a more efficient way of doing this.