<exercise masterit-seed="6995" masterit-slug="S1" masterit-name="Phase Planes"><statement><p>
Draw a phase plane for the following system of ODEs.
</p><me>x'= -2 \, x - 2 \, y </me><me>y'= -4 \, x + 2 \, y + 18 </me><p>Be sure to include and label the following features in your sketch:</p><ul><li>The isoclines <m>x'=0</m> and <m>y'=0</m>.</li><li>Arrow systems describing trajectories of solutions.</li><li>The equillibrium of the system.</li></ul></statement><answer><p>
The isoclines cross at the equillibrium <m> \left(3, -3\right) </m>,
with <m>x'=0</m> having a negative slope
and <m>y'=0</m> having a positive slope.
</p><p>
The right region has a southwest arrow system,
the top region has a northwest arrow system,
the left region has a northeast arrow system, and
the bottom region has a southeast arrow system.
</p></answer></exercise>
