The present thesis deals with the construction of a general solution of weakly delayed systems of linear discrete equations in ${\mathbb R}^3$ of the form
\begin{equation*}
x(k+1)=Ax(k)+Bx(k-m)
\end{equation*}
where $m>0$ is a positive integer, $x\colon \bZ_{-m}^{\infty}\to\bR^3$, $\bZ_{-m}^{\infty} := \{-m, -m+1, \dots, \infty\}$, $k\in\bZ_0^{\infty}$, $A=(a_{ij})$ and $B=(b_{ij})$ are constant $3\times 3$ matrices. The characteristic equations of weakly delayed systems are identical with those of the same systems but without delayed terms. The criteria ensuring that a system is weakly delayed are developed and then specified for every possible case of the Jordan form of matrix $A$. The system is solved by transforming it into a higher-dimensional system but without delays
\begin{equation*}
y(k+1)=\mathcal{A}y(k),
\end{equation*}
where ${\mathrm{dim}}\ y = 3(m+1)$.
Using methods of linear algebra, it is possible to find the Jordan forms of $\mathcal{A}$ depending on the eigenvalues of matrices $A$ and $B$. Therefore, general the solution of the new system can be found and, consequently, the general solution of the initial system deduced.