General Solution Eigenvale

I'm reading my textbook, in the Diagonalization and Eigenvalues section, and am wondering how they get this...

"λI-A = $\displaystyle \left(\begin{array}{ccc} -5 & -5\\ -1 & -1\end{array}\right)$

so the general solution to (λI-A)X = 0 is X = t$\displaystyle \left(\begin{array}{ccc} -1\\ 1\end{array}\right)$ where t is an arbitrary real number."

The book makes it sound as if the general solution of X = t$\displaystyle \left(\begin{array}{ccc} -1\\ 1\end{array}\right)$ is very obvious, but I'm not seeing how it's done.

Could someone enlighten me?