Example 2: In a certain year, the total coal production of a coal mine, apart from a certain amount of coal used for civilian, export, and other non-industrial purposes each year, the rest is reserved for industrial use. According to the standard of industrial coal consumption of a certain industrial city in that year, it can supply 3 such industrial cities for 6 years, or 4 such industrial cities for 5 years (of course, the fixed amount of coal for non-industrial use is deducted each year). How many years can it supply if it only supplies the industrial coal for this one city?
(1978, Chongqing Mathematical Competition)
Solution: Let the total coal production of the mine for the year be $x$, the annual non-industrial coal quota be $y$, and the industrial coal consumption of each industrial city for the year be $z$. Let $p$ be the number of years the coal can supply only one city. According to the problem, we have the system of equations
$$
\left\{\begin{array}{l}
x=6 \times(3 z)+6 y, \\
x=5 \times(4 z)+5 y, \\
p=\frac{x-p y}{2},
\end{array}\right.
$$

which is $\left\{\begin{array}{l}x=18 z+6 y, \\ x=20 z+5 y, \\ p=\frac{x-p y}{2} .\end{array}\right.$
From (1) and (2), we get $y=2 z$.
Then, by eliminating $x$, $y$, and $z$ using equations (1), (3), and (4), we get
$p=30-2 p$. Solving this, we get
$p=10$.
Therefore, the coal can supply only one city for 10 years.