14. Let $\boldsymbol{A}=\left(a_{i j}\right), \boldsymbol{B}=\left(b_{i j}\right)(1 \leqslant i \leqslant n, 1 \leqslant j \leqslant l)$ be two $n$-row $l$-column integer matrices, $m \geqslant 1$. We say matrix $\boldsymbol{A}$ is congruent to matrix $\boldsymbol{B}$ modulo $m$, if $a_{i j} \equiv b_{i j}(\bmod m)$, $1 \leqslant i \leqslant n, 1 \leqslant j \leqslant l$, denoted as $\boldsymbol{A} \equiv \boldsymbol{B}(\bmod m)$. In this way, the system of linear congruences in Problem 13 can be expressed as
$$\left(\begin{array}{ll} a & b \\ c & d \end{array}\right)\binom{x}{y} \equiv\binom{e}{f}(\bmod m)$$
$\Delta$ is the determinant of the matrix $\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)$. When $(\Delta, m)=1$, there is a unique solution
$$\binom{x}{y}=\Delta^{-1}\left(\begin{array}{cc} d & -b \\ -c & a \end{array}\right)\binom{e}{f}(\bmod m) .$$