8.2.2.7 Systems of differential equations

condition: Find a solution to the Cauchy problem for a system of differential equations by the elimination method and the operational method. \[ \left\{\begin{array}{c} x^{\prime}=3 x+2 y \\ y^{\prime \prime}=-10 x-y \end{array}\right. \] \[ x=x(t), y=y(t), x(0)=-1, \quad y(0)=7 \text {. } \]