<exercise masterit-seed="5231" masterit-slug="S2" masterit-name="Linear ODE system with elimination"><statement><p>Find the solution to the given system of IVPs.</p><me> 4 \, {x} + {x'} = 2 \, {y} \hspace{2em}x(0)= 1 </me><me> 0 = -{y'} - 2 \, {x} - 9 \, {y} \hspace{2em}x(0)= 1 </me></statement><answer><me>x= 2 \, e^{\left(-5 \, t\right)} - e^{\left(-8 \, t\right)} </me><me>y= -e^{\left(-5 \, t\right)} + 2 \, e^{\left(-8 \, t\right)} </me></answer></exercise>
