8.3.38 Systems of ordinary differential equations

Condition: Find a particular solution to the system of differential equations that satisfy the given initial conditions: \[ \begin{array}{l} \frac{d x}{d t}=-2 x-4 y, \quad \frac{d y}{d t}=5 x+7 y \\ x(0)=1, \quad y(0)=1 \end{array} \]