The matrix $A=\left[\begin{array}{cc}-23& 10\\ -36& 15\end{array}\right]$ has eigenvalue ${}_1=-3$ with eigenvector vec$(v{)}_1=\left[\begin{array}{c}1\\ 2\end{array}\right]$ and eigenvalue ${}_2=-5$ with eigenvector vec$(v{)}_2=\left[\begin{array}{c}-5\\ -9\end{array}\right].$

Using these eigenvectors, write the general solution vec$(x)(t)$ for the system vec$(x)=$Avec$(x)$ of second order differential equations:

$($Use $a_{-}1,b_{-}1,a_{-}2,b_{-2}$ for the constants $a_1,b_1,a_2,b_2)$