Solve the following system of equations:

$$
\begin{aligned}
& 37 x+92 y=5043, \\
& 92 x+37 y=2568 .
\end{aligned}
$$
We can take advantage of the symmetric structure of the system of equations by adding or subtracting the two equations from each other, instead of using the usual "substitution" methods.

$$
129 x + 129 y = 7611
$$

that is, simplifying by 129,

$$
x + y = 59
$$

Subtracting the first equation from the second,

$$
55 x - 55 y = -2475
$$

that is,

$$
x - y = -45 \text{.}
$$

From (1) and (2),

$$
x = 7, \quad y = 52
$$

János Tóth (Balassagyarmat, Balassa g. I. o. t.)